Maths-
The area bounded by y=cos x, y=x+1 and y=0 in the second quadrant is

Maths-General
- 3/2 sq units
- 2 sq units
- 1 sq unit
- 1/2 sq units
Answer:The correct answer is: 1/2 sq units
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maths-
Area of the region bounded by y=
and y=2 is

Area
sQ. units
Area of the region bounded by y=
and y=2 is

maths-General
Area
sQ. units
maths-
Area of the region bounded by y
is

Area of the region bounded by y
is

maths-General
maths-
The area of the region bounded by y=
and the x-axis is

The area of the region bounded by y=
and the x-axis is

maths-General
physics-
A solid sphere of radius
has moment of inertia
about its geometrical axis. If it is melted into a disc of radius
and thickness
. If its moment of inertia about the tangential axis (which is perpendicular to plane of the disc), is also equal to
, then the value of
is equal to

or
A solid sphere of radius
has moment of inertia
about its geometrical axis. If it is melted into a disc of radius
and thickness
. If its moment of inertia about the tangential axis (which is perpendicular to plane of the disc), is also equal to
, then the value of
is equal to

physics-General
or
maths-
The area of the elliptic quadratic with the semi major axis and semi minor axis as 6 and 4 respectively


The area of the elliptic quadratic with the semi major axis and semi minor axis as 6 and 4 respectively

maths-General

maths-
The area of the region bounded by y=|x-1| and y=1 in sq. units is


The area of the region bounded by y=|x-1| and y=1 in sq. units is

maths-General

physics-
A force of- F
acts on
, the origin of the coordinate system. The torque about the point 1, -(a) is


A force of- F
acts on
, the origin of the coordinate system. The torque about the point 1, -(a) is

physics-General

physics-
A
joint is formed by two identical rods
and
each of mass
and length
in the
plane as shown. Its moment of inertia about axis coinciding with
is

A
joint is formed by two identical rods
and
each of mass
and length
in the
plane as shown. Its moment of inertia about axis coinciding with
is

physics-General
physics-
A binary star consists of two stars
(mass 2.2
) and B (mass 11
), where
is the mass of the sun. They are separated by distance
and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star
about the centre of mass is
A binary star consists of two stars
(mass 2.2
) and B (mass 11
), where
is the mass of the sun. They are separated by distance
and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star
about the centre of mass is
physics-General
physics-
Consider a body, shown in figure, consisting of two identical balls, each of mass
connected by a light rigid rod. If an impulse
is impared to the body at one of its ends, what would be its angular velocity?

Let
be the angular velocity of the rod. Applying ,
Angular impulse = change in angular momentum about centre of mass of the system




Angular impulse = change in angular momentum about centre of mass of the system

Consider a body, shown in figure, consisting of two identical balls, each of mass
connected by a light rigid rod. If an impulse
is impared to the body at one of its ends, what would be its angular velocity?

physics-General
Let
be the angular velocity of the rod. Applying ,
Angular impulse = change in angular momentum about centre of mass of the system




Angular impulse = change in angular momentum about centre of mass of the system

maths-
Assertion (A): If the system of equations
have non zero solution then 
Reason (R): If the system of equations
has a non zero solution then
is singular
Assertion (A): If the system of equations
have non zero solution then 
Reason (R): If the system of equations
has a non zero solution then
is singular
maths-General
physics-
A particle of mass
moves in the
plane with a velocity
along the straight line
. If the angular momentum of the particle with respect to origin
is
when it is at
and
when it is at
, then

From the definition of angular momentum,


Therefore, the magnitude of
is

where
is the distance of closest approach of the particle to the origin. As
is same for both the particles, hence
.

Therefore, the magnitude of
where
A particle of mass
moves in the
plane with a velocity
along the straight line
. If the angular momentum of the particle with respect to origin
is
when it is at
and
when it is at
, then

physics-General
From the definition of angular momentum,


Therefore, the magnitude of
is

where
is the distance of closest approach of the particle to the origin. As
is same for both the particles, hence
.

Therefore, the magnitude of
where
physics-
Four balls each of radius 10 cm and mass 1 kg, 2kg, 3 kg and 4 kg are attached to the periphery of massless plate of radius 1 m. What is moment of inertia of the system about the centre of plate?

Moment of inertia of the system about the centre of plane is given by






Four balls each of radius 10 cm and mass 1 kg, 2kg, 3 kg and 4 kg are attached to the periphery of massless plate of radius 1 m. What is moment of inertia of the system about the centre of plate?

physics-General
Moment of inertia of the system about the centre of plane is given by






physics-
For the given uniform square lamina
, whose centre is 

Let the each side of square lamina is
.
So,
(due to symmetry)
And
(due to symmetry)
Now, according to theorem of perpendicular axis,


(i)
and
(ii)
From Eqs. (i) and (ii), we get



So,
So,
And
Now, according to theorem of perpendicular axis,

and
From Eqs. (i) and (ii), we get
So,
For the given uniform square lamina
, whose centre is 

physics-General
Let the each side of square lamina is
.
So,
(due to symmetry)
And
(due to symmetry)
Now, according to theorem of perpendicular axis,


(i)
and
(ii)
From Eqs. (i) and (ii), we get



So,
So,
And
Now, according to theorem of perpendicular axis,

and
From Eqs. (i) and (ii), we get
So,
physics-
A uniform rod
of length
and mass
is free to rotate about point
. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about
is
, the initial angular acceleration of the rod will be

The moment of inertia of the uniform rod about an axis through one end and perpendicular to its length is

Where
is mass of rod and
is length.
Torque
acting on centre of gravity of rod is given by

or
or
or
Where
Torque
or
or
or
A uniform rod
of length
and mass
is free to rotate about point
. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about
is
, the initial angular acceleration of the rod will be

physics-General
The moment of inertia of the uniform rod about an axis through one end and perpendicular to its length is

Where
is mass of rod and
is length.
Torque
acting on centre of gravity of rod is given by

or
or
or
Where
Torque
or
or
or