Center of Mass and Collision · Physics · TS EAMCET

A ball is allowed to fall freely from a height of 42 m form the ground. If the coefficient of restitution between the ball and the ground is 0.4 , then the total distance travelled by the ball before it comes to rest is

A body of mass ' $m$ ' moving with a velocity of ' $v$ ' collides head on with another body of mass ' 2 m ' at rest. If the coefficient of restitution between the two bodies is ' $~ e$ ', then the ratio of the velocities of the two bodies after collision is

A solid cylinder of mass 2 kg , length 40 cm and radius 10 cm is placed in contact with a solid sphere of mass 0.5 kg and radius 10 cm such that the centres of the two bodies lie along the geometrical axis of the cylinder. The distance of the centre of mass of the system of two bodies from the centre of the sphere is

Two blocks of masses in the ratio $m: n$ are connected by a light inextensible string passing over a frictionless fixed pulley. If the system of the blocks is released from rest, then the acceleration of the centre of mass of the system of the blocks is

( $g=$ acceleration due to gravity)

A ball $A$ of mass 1.2 kg moving with a velocity of $8.4 \mathrm{~ms}^{-1}$ makes one-dimensional elastic collision with a ball $B$ of mass 3.6 kg at rest. The percentage of kinetic energy transferred by ball $A$ to ball $B$ is

A meter scale is balanced on a knife edge at its centre. When two coins, each of mass 9 g are kept one above the other at the 10 cm mark, the scale is found to be balanced at 35 cm . The mass of the meter scale is

A ball $P$ of mass 0.5 kg moving with a velocity of $10 \mathrm{~ms}^{-1}$ collides with another ball $Q$ of mass 1 kg at rest. If the coefficient of restitution is 0.4 , the ratio of the velocities of the balls $P$ and $Q$ after the collision is

A circular plate of radius $r$ is removed from a uniform circular plate $P$ of radius $4 r$ to form a hole. If the distance between the centre of the hole formed and the centre of the plate $P$ is $2 r$, then the distance of mass of the remaining portion from the centre of the plate $P$ is

A ball of mass 1.2 kg moving with a velocity of $12 \mathrm{~ms}^{-1}$ makes one-dimensional collision with anothe stationary ball of mass 1.2 kg . If the coefficient of restitution is $\frac{1}{\sqrt{2}}$, then the ratio of the total kinetic energy of the balls after collision and the initial kinetic energy is

An alphabet $T$ made of two similar thin uniform metal plates of each length $L$ and width $a$ is placed on a horizontal surface as shown in the figure. If the alphabet is vertically inverted, the shift in the position of its centre of mass from the horizontal surface is

Three particles $A, B$ and $C$ of masses $m, 2 m$ and $3 m$ are moving towards north, south and east respectively. If the velocities of the particles $A, B$ and $C$ are $6 \mathrm{~ms}^{-1}$. $12 \mathrm{~ms}^{-1}$ and $8 \mathrm{~ms}^{-1}$ respectively, then the velocity of the centre of mass of the system of particles is

The sphere $A$ of mass $m$ moving with a constant velocity hits another sphere $B$ of mass $2 m$ at rest. If the coefficient of restitution is 0.4 the ratio of the velocities of the spheres $A$ and $B$ after collision is

Four identical particles each of mass $m$ are kept at the four corners of a square of side $a$. If one of the particles is removed, the shift in the position of the centre of mass is

A bomb of mass 16 kg explodes into two pieces of masses 4 kg and 12 kg . The velocity of the 12 kg mass is $4 \mathrm{~ms}^{-1}$. The kinetic energy of the second piece is

A ball falls freely from a height $h$ on a rigid horizontal plane. If the coefficient of restitution is $e$, then the total distance travelled by the ball before hitting the plane second time is

Two blocks of masses 2 kg and 1 kg are tied to the ends of a string which passes over a light frictionless pulley. The blocks are held at the same horizontal level and then released suddenly. The distance traversed by their centre of mass in 2 sec is

(acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A block of mass $M$ moving on a frictionless horizontal surface collides with a spring of spring constant $K$, as shown in the figure. If the spring compresses by a length $L$, then the maximum momentum of the block after the collision is

A body falls freely from a height $h$ on a fixed horizontal plane and rebounds. If $e$ is the coefficient of restitution, the total distance travelled before it comes to rest is

Two blocks of equal masses are tied to the ends of a light string. The string passes over a mass less pulley fixed on frictionless surface as shown in the figure. The acceleration of the centre of mass of the blocks is ( $g=$ acceleration due to gravity)

A system consists of two particles of masses $m_1$ and $m_2$. If the particle of mass $m_1$ is moved towards the centre of mass through a distance $d$, then the distance the second particle should be moved, so as to keep the centre of mass at the same position is

Particle $A$ moving with a velocity $v=10 \mathrm{~m} / \mathrm{s}$ experienced a head on collision with a stationary particle $B$ of the same mass. As a result of collision, the kinetic energy of the system decreased by $1 \%$. The speed of particle $A$ after collision is

Assertion (A) In an elastic collision of two billiard balls, both kinetic energy and linear momentum remain conserved.

Reason (R) During the collision of the balls, as the collision is elastic there is no exchange of energy. Therefore, both energy and momentum are conserved. The correct option among the following is

A moving particle collides with a stationary particle of mass $\frac{1}{n}$ times the mass of moving particle, the fraction of its kinetic energy transferred to the stationary particle is

Four masses are arranged along a circle of radius 1 m as shown in the figure. The centre of mass of this system of masses is at

A moving body with a mass $m_1$ and velocity $u$ strikes a stationary body of mass $m_2$. The masses $m_1$ and $m_2$ should be in the ratio $\frac{m_1}{m_2}$, so as to decrease the velocity of the first body to $\frac{2 u}{3}$ and giving a velocity of $v$ to $m_2$ assuming a perfectly elastic impact. Then, the ratio $\frac{m_1}{m_2}$ is

Two blocks of equal masses are connected with a massless spring of spring constant $2500 \mathrm{~N} / \mathrm{m}^2$ and length 10 cm at rest on the frictionless horizontal plane. If a constant horizontal force 10 N is applied as shown in the figure, find the maximum distance between the blocks.

A bullet of mass 25 g moves horizontally at a speed of $250 \mathrm{~m} / \mathrm{s}$ is fired into a wooden block of mass 1 kg suspended by a long string. The bullet crosses the block and emerges on the other side. If the centre of the mass of the block rises through a height of 20 cm . The speed of the bullet as it emerges from the block is (take, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A circular hole of radius 3 cm is cut out from a uniform circular disc of radius 6 cm . The centre of the hole is at 3 cm , from the centre of the original disc. The distance of centre of gravity of the resulting flat body from the centre of the original disc is