A small body of mass is slides down from the top of a hemispher-Turito

General

Easy

Physics-

A small body of mass $m$ slides down from the top of a hemisphere of radius $r$ . The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is

Physics-General

$\frac{1}{2} g t^{2}$
$\frac{2}{3} r$
$\frac{v^{2}}{2 g}$
$\frac{3}{2} r$

Answer:The correct answer is: $fraction numerator 2 over denominator 3 end fraction r$

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Related Questions to study

General

physics-

Average torque on a projectile of mass $m$ , initial speed $u$ and angles of projection $theta$ , between initial and final position $P$ and $Q$ as shown in figure about the point of projection is

Time of flight.

T equals fraction numerator 2 u sin invisible function application theta over denominator g end fraction

Horizontal range,

R equals fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction

Change in angular momentum,

open vertical bar d stack L with rightwards arrow on top close vertical bar equals open vertical bar stack L with rightwards arrow on top subscript f end subscript minus stack L with rightwards arrow on top subscript i end subscript close vertical bar

about point of projection

equals left parenthesis m u sin invisible function application theta right parenthesis cross times fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction

equals fraction numerator m u to the power of 3 end exponent sin invisible function application theta sin invisible function application 2 theta over denominator g end fraction

T o r q u e blank open vertical bar stack tau with rightwards arrow on top close vertical bar equals fraction numerator c h a n g e blank i n blank a n g u l a r blank m o m e n t u m over denominator t i m e blank o f blank f l i g h t end fraction

equals open vertical bar fraction numerator d stack L with rightwards arrow on top over denominator T end fraction close vertical bar

Average torque on a projectile of mass $m$ , initial speed $u$ and angles of projection $theta$ , between initial and final position $P$ and $Q$ as shown in figure about the point of projection is

physics-General

Time of flight.

T equals fraction numerator 2 u sin invisible function application theta over denominator g end fraction

Horizontal range,

R equals fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction

Change in angular momentum,

open vertical bar d stack L with rightwards arrow on top close vertical bar equals open vertical bar stack L with rightwards arrow on top subscript f end subscript minus stack L with rightwards arrow on top subscript i end subscript close vertical bar

about point of projection

equals left parenthesis m u sin invisible function application theta right parenthesis cross times fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction

equals fraction numerator m u to the power of 3 end exponent sin invisible function application theta sin invisible function application 2 theta over denominator g end fraction

T o r q u e blank open vertical bar stack tau with rightwards arrow on top close vertical bar equals fraction numerator c h a n g e blank i n blank a n g u l a r blank m o m e n t u m over denominator t i m e blank o f blank f l i g h t end fraction

equals open vertical bar fraction numerator d stack L with rightwards arrow on top over denominator T end fraction close vertical bar

General

physics-

Three balls are dropped from the top of a building with equal speed at different angles. When the balls strike ground their velocities are $v subscript 1 end subscript comma v blank subscript 2 end subscript$ and $v subscript 3 end subscript$ respectively, then

All the balls are projected from the same height, therefore their velocities will be equal.

S o comma blank v subscript 1 end subscript equals v subscript 2 end subscript equals v subscript 3 end subscript

Three balls are dropped from the top of a building with equal speed at different angles. When the balls strike ground their velocities are $v subscript 1 end subscript comma v blank subscript 2 end subscript$ and $v subscript 3 end subscript$ respectively, then

physics-General

All the balls are projected from the same height, therefore their velocities will be equal.

S o comma blank v subscript 1 end subscript equals v subscript 2 end subscript equals v subscript 3 end subscript

General

maths-

The equation of the plane containing the line $fraction numerator x with not stretchy bar on top minus alpha over denominator 1 end fraction equals fraction numerator y minus beta over denominator m end fraction equals fraction numerator z minus gamma over denominator n end fraction text is end text stack a with _ below with _ below left parenthesis x minus alpha right parenthesis plus b left parenthesis y minus beta right parenthesis plus c left parenthesis z minus gamma right parenthesis equals 0$ where al + bm + cn is equal to

Since these two lines are intersecting so shortest distance between the lines will be 0.
Hence (c) is the correct answer.

The equation of the plane containing the line $fraction numerator x with not stretchy bar on top minus alpha over denominator 1 end fraction equals fraction numerator y minus beta over denominator m end fraction equals fraction numerator z minus gamma over denominator n end fraction text is end text stack a with _ below with _ below left parenthesis x minus alpha right parenthesis plus b left parenthesis y minus beta right parenthesis plus c left parenthesis z minus gamma right parenthesis equals 0$ where al + bm + cn is equal to

maths-General

Since these two lines are intersecting so shortest distance between the lines will be 0.
Hence (c) is the correct answer.

General

physics-

A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out length $s equals t to the power of 3 end exponent plus 5 comma$ where $s$ is in metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2s is nearly

G i v e n comma blank s equals t to the power of 3 end exponent plus 5

S p e e d comma blank v equals fraction numerator d s over denominator d t end fraction equals 3 t to the power of 2 end exponent

a n d blank r a t e blank o f blank c h a n g e blank o f blank s p e e d comma blank a subscript t end subscript equals fraction numerator d v over denominator d t end fraction equals 6 t

therefore T a n g e n t i a l blank a c c e l e r a t i o n blank a t blank t equals 2 blank s comma

a subscript t end subscript equals 6 cross times 2 equals 12 blank m s to the power of negative 2 end exponent

a n d blank a t blank t equals 2 s comma blank v equals 3 left parenthesis 2 right parenthesis to the power of 2 end exponent equals 12 m s to the power of negative 1 end exponent

therefore C e n t r i p e t a l blank a c c e l e r a t i o n comma blank a subscript c end subscript equals fraction numerator v to the power of 2 end exponent over denominator R end fraction equals fraction numerator 144 over denominator 20 end fraction m s to the power of negative 2 end exponent

therefore N e t blank a c c e l e r a t i o n equals a subscript t end subscript superscript 2 end superscript plus a subscript i end subscript superscript 2 end superscript almost equal to 14 m s to the power of negative 2 end exponent

A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out length $s equals t to the power of 3 end exponent plus 5 comma$ where $s$ is in metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2s is nearly

physics-General

G i v e n comma blank s equals t to the power of 3 end exponent plus 5

S p e e d comma blank v equals fraction numerator d s over denominator d t end fraction equals 3 t to the power of 2 end exponent

a n d blank r a t e blank o f blank c h a n g e blank o f blank s p e e d comma blank a subscript t end subscript equals fraction numerator d v over denominator d t end fraction equals 6 t

therefore T a n g e n t i a l blank a c c e l e r a t i o n blank a t blank t equals 2 blank s comma

a subscript t end subscript equals 6 cross times 2 equals 12 blank m s to the power of negative 2 end exponent

a n d blank a t blank t equals 2 s comma blank v equals 3 left parenthesis 2 right parenthesis to the power of 2 end exponent equals 12 m s to the power of negative 1 end exponent

therefore C e n t r i p e t a l blank a c c e l e r a t i o n comma blank a subscript c end subscript equals fraction numerator v to the power of 2 end exponent over denominator R end fraction equals fraction numerator 144 over denominator 20 end fraction m s to the power of negative 2 end exponent

therefore N e t blank a c c e l e r a t i o n equals a subscript t end subscript superscript 2 end superscript plus a subscript i end subscript superscript 2 end superscript almost equal to 14 m s to the power of negative 2 end exponent

General

physics-

A piece of wire is bent in the shape of a parabola $y = k x^{2} (y$ -axis vertical) with a bead of mass $m$ on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the $x$ -axis with a constant acceleration $a$ . The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the $y$ -axis is

m a \cos θ = m g \cos (90 - θ)

\Rightarrow \frac{a}{g} = \tan θ \Rightarrow \frac{a}{g} = \frac{d y}{d x}

\Rightarrow \frac{d}{d x} {(k x)}^{2} = \frac{a}{g} \Rightarrow x = \frac{a}{2 g k}

A piece of wire is bent in the shape of a parabola $y = k x^{2} (y$ -axis vertical) with a bead of mass $m$ on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the $x$ -axis with a constant acceleration $a$ . The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the $y$ -axis is

physics-General

m a \cos θ = m g \cos (90 - θ)

\Rightarrow \frac{a}{g} = \tan θ \Rightarrow \frac{a}{g} = \frac{d y}{d x}

\Rightarrow \frac{d}{d x} {(k x)}^{2} = \frac{a}{g} \Rightarrow x = \frac{a}{2 g k}

General

physics-

A string of length $L$ is fixed at one end and the string makes $fraction numerator 2 over denominator pi end fraction$ rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is

T sin invisible function application theta equals M omega to the power of 2 end exponent R

(i)

T sin invisible function application theta equals M omega to the power of 2 end exponent L blank s i n blank theta

(ii)

T equals M omega to the power of 2 end exponent L

equals M bullet 4 pi to the power of 2 end exponent n to the power of 2 end exponent L

equals M bullet 4 pi to the power of 2 end exponent open parentheses fraction numerator 2 over denominator pi end fraction close parentheses to the power of 2 end exponent L

equals 16 blank M L

A string of length $L$ is fixed at one end and the string makes $fraction numerator 2 over denominator pi end fraction$ rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is

physics-General

T sin invisible function application theta equals M omega to the power of 2 end exponent R

(i)

T sin invisible function application theta equals M omega to the power of 2 end exponent L blank s i n blank theta

(ii)

T equals M omega to the power of 2 end exponent L

equals M bullet 4 pi to the power of 2 end exponent n to the power of 2 end exponent L

equals M bullet 4 pi to the power of 2 end exponent open parentheses fraction numerator 2 over denominator pi end fraction close parentheses to the power of 2 end exponent L

equals 16 blank M L

General

physics-

A bob of mass M is suspended by a massless string of length L. The horizontal velocity $v$ at position A is just sufficient to make it reach the point B. The angle $θ$ at which the speed of the bob is half of that at A, satisfies

Velocity of the bob at the point A

v = \sqrt{5 g L}

(i)

{(\frac{v}{2})}^{2} = v^{2} - 2 g h (i i)

h = L (1 - \cos θ) (i i i)

S o l v i n g E q s . (i), (i i) a n d (i i i), w e g e t

\cos θ = - \frac{7}{8}

o r θ = {c o s}^{- 1} (- \frac{7}{8}) = 151 °

A bob of mass M is suspended by a massless string of length L. The horizontal velocity $v$ at position A is just sufficient to make it reach the point B. The angle $θ$ at which the speed of the bob is half of that at A, satisfies

physics-General

Velocity of the bob at the point A

v = \sqrt{5 g L}

(i)

{(\frac{v}{2})}^{2} = v^{2} - 2 g h (i i)

h = L (1 - \cos θ) (i i i)

S o l v i n g E q s . (i), (i i) a n d (i i i), w e g e t

\cos θ = - \frac{7}{8}

o r θ = {c o s}^{- 1} (- \frac{7}{8}) = 151 °

General

maths-

The shortest distance between the two straight line $\frac{x - 4 / 3}{2} = \frac{y + 6 / 5}{3} = \frac{z - 3 / 2}{4}$ and $\frac{5 y + 6}{8} = \frac{2 z - 3}{9} = \frac{3 x - 4}{5}$ is

maths-General

General

physics-

A thin prism $P subscript 1 end subscript$ with angle $6 to the power of ring operator end exponent$ and made from glass of refractive index 1.54 is combined with another thin prism $P subscript 2 end subscript$ of refractive index 1.72 to produce dispersion without deviation. The angle of prism $P subscript 2 end subscript$ will be

fraction numerator A to the power of ´ end exponent over denominator A end fraction equals fraction numerator left parenthesis mu subscript y end subscript minus 1 right parenthesis over denominator left parenthesis mu subscript y ´ end subscript minus 1 right parenthesis end fraction rightwards double arrow fraction numerator A to the power of ´ end exponent over denominator 6 end fraction equals negative fraction numerator left parenthesis 1.54 minus 1 right parenthesis over denominator left parenthesis 1.72 minus 1 right parenthesis end fraction

Þ A'

equals negative 4.5 to the power of o end exponent equals 4 to the power of o end exponent 3 0 to the power of ´ end exponent

A thin prism $P subscript 1 end subscript$ with angle $6 to the power of ring operator end exponent$ and made from glass of refractive index 1.54 is combined with another thin prism $P subscript 2 end subscript$ of refractive index 1.72 to produce dispersion without deviation. The angle of prism $P subscript 2 end subscript$ will be

physics-General

fraction numerator A to the power of ´ end exponent over denominator A end fraction equals fraction numerator left parenthesis mu subscript y end subscript minus 1 right parenthesis over denominator left parenthesis mu subscript y ´ end subscript minus 1 right parenthesis end fraction rightwards double arrow fraction numerator A to the power of ´ end exponent over denominator 6 end fraction equals negative fraction numerator left parenthesis 1.54 minus 1 right parenthesis over denominator left parenthesis 1.72 minus 1 right parenthesis end fraction

Þ A'

equals negative 4.5 to the power of o end exponent equals 4 to the power of o end exponent 3 0 to the power of ´ end exponent

General

maths-

The value of $\int_{0}^{100} {\sqrt{x}} d x$ (where {x} is the fractional part of x) is

maths-General

General

physics-

A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if $theta equals 4 5 to the power of o end exponent$ . The index of refraction of glass is

For total internal reflection

theta greater than C

rightwards double arrow

sin invisible function application theta greater than sin invisible function application C rightwards double arrow sin invisible function application theta greater than fraction numerator 1 over denominator mu end fraction

mu greater than fraction numerator 1 over denominator sin invisible function application theta end fraction rightwards double arrow mu greater than fraction numerator 1 over denominator sin invisible function application 4 5 to the power of o end exponent end fraction rightwards double arrow mu greater than square root of 2 rightwards double arrow mu greater than 1.41

A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if $theta equals 4 5 to the power of o end exponent$ . The index of refraction of glass is

physics-General

For total internal reflection

theta greater than C

rightwards double arrow

sin invisible function application theta greater than sin invisible function application C rightwards double arrow sin invisible function application theta greater than fraction numerator 1 over denominator mu end fraction

mu greater than fraction numerator 1 over denominator sin invisible function application theta end fraction rightwards double arrow mu greater than fraction numerator 1 over denominator sin invisible function application 4 5 to the power of o end exponent end fraction rightwards double arrow mu greater than square root of 2 rightwards double arrow mu greater than 1.41

General

maths-

The value of $\int_{0}^{1} | \sin 2 π x | ∣ d x$ is equal to

Given plane y + z + 1 = 0 is parallel to x-axis as 0.1 + 1.0 + 1.0 = 0 but normal to the plane will be perpendicular to x-axis. Hence (c) is the correct answer.

The value of $\int_{0}^{1} | \sin 2 π x | ∣ d x$ is equal to

maths-General

Given plane y + z + 1 = 0 is parallel to x-axis as 0.1 + 1.0 + 1.0 = 0 but normal to the plane will be perpendicular to x-axis. Hence (c) is the correct answer.

General

maths-

Let $f : R \to R, f (x) = \{\begin{matrix} | x - [x] |, [x] \\ | x - [x + 1] |, [x] \end{matrix}$ $\begin{aligned} is odd \\ 1 is even where [.] \end{aligned}$ denotes greatest integer function, then $\int_{- 2}^{4} f (x) d x$ is equal to

Since these two lines are intersecting so shortest distance between the lines will be 0. Hence (c) is the correct answer.

Let $f : R \to R, f (x) = \{\begin{matrix} | x - [x] |, [x] \\ | x - [x + 1] |, [x] \end{matrix}$ $\begin{aligned} is odd \\ 1 is even where [.] \end{aligned}$ denotes greatest integer function, then $\int_{- 2}^{4} f (x) d x$ is equal to

maths-General

Since these two lines are intersecting so shortest distance between the lines will be 0. Hence (c) is the correct answer.

General

physics-

Which of the following diagrams, shows correctly the dispersion of white light by a prism

Because in dispersion of white light, the rays of different colours are not parallel to each other. Also deviation takes place in same direction.

Which of the following diagrams, shows correctly the dispersion of white light by a prism

physics-General

Because in dispersion of white light, the rays of different colours are not parallel to each other. Also deviation takes place in same direction.

General

maths-

$\int_{- π / 4}^{π / 4} \frac{e^{x} (x \sin x)}{e^{2 x} - 1} d x$ is equal to

Let direction cosines of straight line be l, m, n \ 4l + m + n = 0 l – 2m + n = 0 Þ

\frac{l}{3} = \frac{m}{- 3} = \frac{n}{- 9}

\frac{l}{- 1} = \frac{m}{+ 1} = \frac{n}{3}

\ Equation of straight line is

\frac{x - 2}{- 1} = \frac{y + 1}{1} = \frac{z + 1}{3}

. Hence (c) is the correct choice.

$\int_{- π / 4}^{π / 4} \frac{e^{x} (x \sin x)}{e^{2 x} - 1} d x$ is equal to

maths-General

Let direction cosines of straight line be l, m, n \ 4l + m + n = 0 l – 2m + n = 0 Þ

\frac{l}{3} = \frac{m}{- 3} = \frac{n}{- 9}

\frac{l}{- 1} = \frac{m}{+ 1} = \frac{n}{3}

\ Equation of straight line is

\frac{x - 2}{- 1} = \frac{y + 1}{1} = \frac{z + 1}{3}

. Hence (c) is the correct choice.

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Can’t find what you’re looking for?

A small body of mass $m$ slides down from the top of a hemisphere of radius $r$ . The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is

$\frac{1}{2} g t^{2}$
$\frac{2}{3} r$
$\frac{v^{2}}{2 g}$
$\frac{3}{2} r$

Answer:The correct answer is: $fraction numerator 2 over denominator 3 end fraction r$

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Average torque on a projectile of mass $m$ , initial speed $u$ and angles of projection $theta$ , between initial and final position $P$ and $Q$ as shown in figure about the point of projection is

Average torque on a projectile of mass $m$ , initial speed $u$ and angles of projection $theta$ , between initial and final position $P$ and $Q$ as shown in figure about the point of projection is

Three balls are dropped from the top of a building with equal speed at different angles. When the balls strike ground their velocities are $v subscript 1 end subscript comma v blank subscript 2 end subscript$ and $v subscript 3 end subscript$ respectively, then

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A string of length $L$ is fixed at one end and the string makes $fraction numerator 2 over denominator pi end fraction$ rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is

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A bob of mass M is suspended by a massless string of length L. The horizontal velocity $v$ at position A is just sufficient to make it reach the point B. The angle $θ$ at which the speed of the bob is half of that at A, satisfies

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The shortest distance between the two straight line $\frac{x - 4 / 3}{2} = \frac{y + 6 / 5}{3} = \frac{z - 3 / 2}{4}$ and $\frac{5 y + 6}{8} = \frac{2 z - 3}{9} = \frac{3 x - 4}{5}$ is

The shortest distance between the two straight line $\frac{x - 4 / 3}{2} = \frac{y + 6 / 5}{3} = \frac{z - 3 / 2}{4}$ and $\frac{5 y + 6}{8} = \frac{2 z - 3}{9} = \frac{3 x - 4}{5}$ is

The value of $\int_{0}^{100} {\sqrt{x}} d x$ (where {x} is the fractional part of x) is

The value of $\int_{0}^{100} {\sqrt{x}} d x$ (where {x} is the fractional part of x) is

A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if $theta equals 4 5 to the power of o end exponent$ . The index of refraction of glass is

A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if $theta equals 4 5 to the power of o end exponent$ . The index of refraction of glass is

The value of $\int_{0}^{1} | \sin 2 π x | ∣ d x$ is equal to

The value of $\int_{0}^{1} | \sin 2 π x | ∣ d x$ is equal to

Let $f : R \to R, f (x) = \{\begin{matrix} | x - [x] |, [x] \\ | x - [x + 1] |, [x] \end{matrix}$ $\begin{aligned} is odd \\ 1 is even where [.] \end{aligned}$ denotes greatest integer function, then $\int_{- 2}^{4} f (x) d x$ is equal to

Let $f : R \to R, f (x) = \{\begin{matrix} | x - [x] |, [x] \\ | x - [x + 1] |, [x] \end{matrix}$ $\begin{aligned} is odd \\ 1 is even where [.] \end{aligned}$ denotes greatest integer function, then $\int_{- 2}^{4} f (x) d x$ is equal to

Which of the following diagrams, shows correctly the dispersion of white light by a prism

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$\int_{- π / 4}^{π / 4} \frac{e^{x} (x \sin x)}{e^{2 x} - 1} d x$ is equal to

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A small body of mass slides down from the top of a hemisphere of radius . The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is

Answer:The correct answer is:

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Three balls are dropped from the top of a building with equal speed at different angles. When the balls strike ground their velocities are and respectively, then

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A string of length is fixed at one end and the string makes rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is

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A small body of mass $m$ slides down from the top of a hemisphere of radius $r$ . The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is

Answer:The correct answer is: $fraction numerator 2 over denominator 3 end fraction r$

Average torque on a projectile of mass $m$ , initial speed $u$ and angles of projection $theta$ , between initial and final position $P$ and $Q$ as shown in figure about the point of projection is

Average torque on a projectile of mass $m$ , initial speed $u$ and angles of projection $theta$ , between initial and final position $P$ and $Q$ as shown in figure about the point of projection is

Three balls are dropped from the top of a building with equal speed at different angles. When the balls strike ground their velocities are $v subscript 1 end subscript comma v blank subscript 2 end subscript$ and $v subscript 3 end subscript$ respectively, then

Three balls are dropped from the top of a building with equal speed at different angles. When the balls strike ground their velocities are $v subscript 1 end subscript comma v blank subscript 2 end subscript$ and $v subscript 3 end subscript$ respectively, then

A string of length $L$ is fixed at one end and the string makes $fraction numerator 2 over denominator pi end fraction$ rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is

A string of length $L$ is fixed at one end and the string makes $fraction numerator 2 over denominator pi end fraction$ rev/s around the vertical axis through, the fixed and as shown in the figure, then tension in the string is

A bob of mass M is suspended by a massless string of length L. The horizontal velocity $v$ at position A is just sufficient to make it reach the point B. The angle $θ$ at which the speed of the bob is half of that at A, satisfies

A bob of mass M is suspended by a massless string of length L. The horizontal velocity $v$ at position A is just sufficient to make it reach the point B. The angle $θ$ at which the speed of the bob is half of that at A, satisfies

The shortest distance between the two straight line $\frac{x - 4 / 3}{2} = \frac{y + 6 / 5}{3} = \frac{z - 3 / 2}{4}$ and $\frac{5 y + 6}{8} = \frac{2 z - 3}{9} = \frac{3 x - 4}{5}$ is

The shortest distance between the two straight line $\frac{x - 4 / 3}{2} = \frac{y + 6 / 5}{3} = \frac{z - 3 / 2}{4}$ and $\frac{5 y + 6}{8} = \frac{2 z - 3}{9} = \frac{3 x - 4}{5}$ is

The value of $\int_{0}^{100} {\sqrt{x}} d x$ (where {x} is the fractional part of x) is

The value of $\int_{0}^{100} {\sqrt{x}} d x$ (where {x} is the fractional part of x) is

A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if $theta equals 4 5 to the power of o end exponent$ . The index of refraction of glass is

A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if $theta equals 4 5 to the power of o end exponent$ . The index of refraction of glass is

The value of $\int_{0}^{1} | \sin 2 π x | ∣ d x$ is equal to

The value of $\int_{0}^{1} | \sin 2 π x | ∣ d x$ is equal to

Let $f : R \to R, f (x) = \{\begin{matrix} | x - [x] |, [x] \\ | x - [x + 1] |, [x] \end{matrix}$ $\begin{aligned} is odd \\ 1 is even where [.] \end{aligned}$ denotes greatest integer function, then $\int_{- 2}^{4} f (x) d x$ is equal to

Let $f : R \to R, f (x) = \{\begin{matrix} | x - [x] |, [x] \\ | x - [x + 1] |, [x] \end{matrix}$ $\begin{aligned} is odd \\ 1 is even where [.] \end{aligned}$ denotes greatest integer function, then $\int_{- 2}^{4} f (x) d x$ is equal to

$\int_{- π / 4}^{π / 4} \frac{e^{x} (x \sin x)}{e^{2 x} - 1} d x$ is equal to

$\int_{- π / 4}^{π / 4} \frac{e^{x} (x \sin x)}{e^{2 x} - 1} d x$ is equal to