Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Physics-

General

Easy

Question

The blocks $A$ and $B$ , each of mass $m$ , are connected by massless spring of natural length $L$ and spring constant $k$ . The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block $C$ , also of mass $m$ , moves on the floor with a speed $v$ along the line joining $A$ and $B$ , and collides with $A$ . Then

The KE o the $A - B$ system, at maximum compression of the spring, is zero
The KE of the $A - B$ system, at maximum compression of the spring is $\frac{1}{4} m v^{2}$
The maximum compression of the spring is $v \sqrt{\frac{m}{k}}$
The maximum compression of the spring is $v \sqrt{\frac{m}{2 k}}$

The correct answer is: The maximum compression of the spring is $v square root of fraction numerator m over denominator 2 k end fraction end root$

The compression of spring is maximum when velocities of both blocks $A$ and $B$ is same. Let it be $v subscript 0 end subscript$ , then from conservation law of momentum
$m v equals m v subscript 0 end subscript plus m v subscript 0 end subscript equals 2 m v subscript 0 end subscript rightwards double arrow v subscript 0 end subscript equals fraction numerator v over denominator 2 end fraction$
$therefore$ kinetic energy of $A minus B$ system at that stage
$equals fraction numerator 1 over denominator 2 end fraction open parentheses m plus m close parentheses cross times open parentheses fraction numerator v over denominator 2 end fraction close parentheses to the power of 2 end exponent equals fraction numerator m v to the power of 2 end exponent over denominator 4 end fraction$
Further loss in KE> = gain in elastic potential energy
$i e$ , $fraction numerator 1 over denominator 2 end fraction m v to the power of 2 end exponent minus fraction numerator 1 over denominator 4 end fraction m v to the power of 2 end exponent equals fraction numerator 1 over denominator 4 end fraction m v to the power of 2 end exponent equals fraction numerator 1 over denominator 2 end fraction k x to the power of 2 end exponent$
$rightwards double arrow blank x equals v square root of fraction numerator m over denominator 2 k end fraction end root$

Related Questions to study

Find the velocity of centre of the system shown in the figure.

Find the velocity of centre of the system shown in the figure.

physics-General

Two blocks $A$ and $B$ are connected by a massless string (shown in figure). A force of 30 N is applied on block $B$ . The distance travelled by centre of mass in 2 s starting from rest is

Two blocks $A$ and $B$ are connected by a massless string (shown in figure). A force of 30 N is applied on block $B$ . The distance travelled by centre of mass in 2 s starting from rest is

physics-General

Three rods of the same mass are placed as shown in figure. What will be the coordinates of centre of mass of the system?

Three rods of the same mass are placed as shown in figure. What will be the coordinates of centre of mass of the system?

physics-General

parallel

If $sum from n equals 3 to straight infinity of fraction numerator blank to the power of n C subscript 3 over denominator n factorial end fraction equals a times e to the power of b plus c$ then descending order of $a comma b comma c$
is

If $sum from n equals 3 to straight infinity of fraction numerator blank to the power of n C subscript 3 over denominator n factorial end fraction equals a times e to the power of b plus c$ then descending order of $a comma b comma c$
is

A disc is rolling (without slipping) on a horizontal surface $C$ is its centre and $Q$ and $P$ are two points equidistant from $C$ . Let $v subscript P end subscript$ , $v subscript Q end subscript$ and $v subscript C end subscript$ be the magnitude of velocities of pints $P comma blank Q$ and $C$ respectively, then

A disc is rolling (without slipping) on a horizontal surface $C$ is its centre and $Q$ and $P$ are two points equidistant from $C$ . Let $v subscript P end subscript$ , $v subscript Q end subscript$ and $v subscript C end subscript$ be the magnitude of velocities of pints $P comma blank Q$ and $C$ respectively, then

physics-General

The acceleration of the center of mass of a uniform solid disc rolling down an inclined plane of angle $alpha$ is

The acceleration of the center of mass of a uniform solid disc rolling down an inclined plane of angle $alpha$ is

Physics-General

parallel

A solid sphere of mass $m$ rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is $v$ . The kinetic energy of the sphere at the bottom is

A solid sphere of mass $m$ rolls down an inclined plane without slipping, starting from rest at the top of an inclined plane. The linear speed of the sphere at the bottom of the inclined plane is $v$ . The kinetic energy of the sphere at the bottom is

Physics-General

The moments of inertia of two freely rotating bodies $A$ and $B$ are $I subscript A end subscript$ and $I subscript B end subscript$ respectively. $I subscript A end subscript greater than I subscript B end subscript$ and their angular momenta are equal. If $K subscript A end subscript$ and $K subscript B end subscript$ are their kinetic energies, then

The moments of inertia of two freely rotating bodies $A$ and $B$ are $I subscript A end subscript$ and $I subscript B end subscript$ respectively. $I subscript A end subscript greater than I subscript B end subscript$ and their angular momenta are equal. If $K subscript A end subscript$ and $K subscript B end subscript$ are their kinetic energies, then

Physics-General

Famous palaeonotologist/Palaeobotanist of India was:

Famous palaeonotologist/Palaeobotanist of India was:

parallel

A small object of uniform density roll up a curved surface with an initial velocity $v$ . If reaches up to a maximum height of $fraction numerator 3 v to the power of 2 end exponent over denominator 4 g end fraction$ with respect to the initial position. The object is

A small object of uniform density roll up a curved surface with an initial velocity $v$ . If reaches up to a maximum height of $fraction numerator 3 v to the power of 2 end exponent over denominator 4 g end fraction$ with respect to the initial position. The object is

physics-General

A uniform rod $A B$ of length $l$ and mass $m$ is free to rotate about point $A$ . The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about $A$ is $fraction numerator m l to the power of 2 end exponent over denominator 3 end fraction$ , the initial angular acceleration of the rod will be

A uniform rod $A B$ of length $l$ and mass $m$ is free to rotate about point $A$ . The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about $A$ is $fraction numerator m l to the power of 2 end exponent over denominator 3 end fraction$ , the initial angular acceleration of the rod will be

physics-General

A particle of mass $m$ moves in the $X Y$ plane with a velocity $v$ along the straight line $A B$ . If the angular momentum of the particle with respect to origin $O$ is $L subscript A end subscript$ when it is at $A$ and $L subscript B end subscript$ when it is at $B$ , then

A particle of mass $m$ moves in the $X Y$ plane with a velocity $v$ along the straight line $A B$ . If the angular momentum of the particle with respect to origin $O$ is $L subscript A end subscript$ when it is at $A$ and $L subscript B end subscript$ when it is at $B$ , then

physics-General

parallel

Assertion (A): If the system of equations $3 x minus 2 y plus z equals 0 comma lambda x minus 14 y plus 15 z equals 0 comma x plus 2 y minus 3 z equals 0$ have non zero solution then $lambda equals 5$
Reason (R): If the system of equations $A X equals 0$ has a non zero solution then $bold italic A$ is singular

Assertion (A): If the system of equations $3 x minus 2 y plus z equals 0 comma lambda x minus 14 y plus 15 z equals 0 comma x plus 2 y minus 3 z equals 0$ have non zero solution then $lambda equals 5$
Reason (R): If the system of equations $A X equals 0$ has a non zero solution then $bold italic A$ is singular

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

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

physics-General

A binary star consists of two stars $A$ (mass 2.2 $M subscript s end subscript$ ) and B (mass 11 $M subscript s end subscript$ ), where $M subscript s end subscript$ is the mass of the sun. They are separated by distance $d$ 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 $B$ about the centre of mass is

A binary star consists of two stars $A$ (mass 2.2 $M subscript s end subscript$ ) and B (mass 11 $M subscript s end subscript$ ), where $M subscript s end subscript$ is the mass of the sun. They are separated by distance $d$ 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 $B$ about the centre of mass is

physics-General

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.