iCON Education - Center of Mass and Collision AP-EAPCET Test

A body of mass 2 kg is moving towards north with a velocity of $20 \mathrm{~ms}^{-1}$ and another body of mass 3 kg is moving towards east with a velocity of $10 \mathrm{~ms}^{-1}$. The magnitude of the velocity of the centre of mass of the system of the two bodies is

$20 \mathrm{~ms}^{-1}$

$10 \mathrm{~ms}^{-1}$

$15 \mathrm{~ms}^{-1}$

$2 \sqrt{5} \mathrm{~ms}^{-1}$

A body falls freely on to a hard horizontal surface. If the coefficient of restitution between the surface and the body is 0.8 , then the ratio of the maximum height to which the body rises after second impact and the initial height of the body is

Two bodies of masses $M$ and $4 M$ initially at rest, start moving towards each other due to their mutual attraction. The velocity of their centre of mass when the first body attains a velocity $v_0$ is

A body of mass ' $m$ ' moving along a straight line collides with a stationary body of mass ' $2 m^{\prime}$. After collision if the two bodies move together with the same velocity, then the fraction of kinetic energy lost in the process is

A disc of mass 0.2 kg is kept floating in air without falling by vertically firing bullets each of mass 0.05 kg on the disc at the rate of 10 bullets per every second. If the bullets rebound with the same speed, then the speed of each bullet is

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

$2 \mathrm{~ms}^{-1}$

$10 \mathrm{~m} \mathrm{~s}^{-1}$

$20 \mathrm{~ms}^{-1}$

$1 \mathrm{~ms}^{-1}$

A body moving along a straight line collides another body of same mass moving in the same direction with half of the velocity of the first body. If the coefficient of restitution between the two bodies is 0.5 , then the ratio of the velocities of the two bodies after collision is (Treat the collision as one dimensional)

The co-ordinates of the centre of mass of a uniform $L$ shaped plate of mass 3 kg shown in the figure is

AP EAPCET 2025 - 23rd May Evening Shift Physics - Center of Mass and Collision Question 7 English

$\left(\frac{5}{6} m, \frac{5}{6} m\right)$

$\left(\frac{3}{2} m, \frac{3}{2} m\right)$

$\left(\frac{1}{2} m, \frac{1}{2} m\right)$

$\left(\frac{6}{5} m, \frac{6}{5} m\right)$

Three blocks $A, B$ and $C$ are arranged as shown in the figure such that the distance between two successive blocks is 10 m . Block $A$ is displaced towards block $B$ by 2 m and block $C$ is displaced towards block $B$ by 3 m . The distance through which the block $B$ should be moved, so that the centre of mass of the system does not change is

AP EAPCET 2025 - 22nd May Evening Shift Physics - Center of Mass and Collision Question 8 English

1.4 m , towards block C

1.5 m , towards block A

2 m , towards block A

1 m , towards block C

Two balls each of mass 250 g moving in opposite directions each with a speed $16 \mathrm{~ms}^{-1}$ collide and rebound with the same speeds. The impulse imparted to one ball due to the other is

$4 \mathrm{~kg} \mathrm{~ms}^{-1}$

$16 \mathrm{~kg} \mathrm{~ms}^{-1}$

$8 \mathrm{~kg} \mathrm{~ms}^{-1}$

$2 \mathrm{~kg} \mathrm{~ms}^{-1}$

A block of mass 10 kg moving with a speed of $5 \hat{\mathrm{i}} \mathrm{ms}^{-1}$ on a frictionless horizontal surface suddenly explodes into two pieces. If one piece with mass 4 kg moves with a speed of $10 \hat{\mathbf{i}} \mathrm{~ms}^{-1}$, then the velocity of the second piece is

$7.67 \mathrm{~ms}^{-1}$

$1.67 \mathrm{~ms}^{-1}$

$6.67 \mathrm{~s} \mathrm{~ms}^{-1}$

$2.67 \mathrm{~ms}^{-1}$

A steel sphere of radius 1.2 cm collides a second steel sphere at rest. If the collision is elastic and after the collision the first sphere continues to move in its initial direction with a velocity of $\frac{7}{9}$ times its initial velocity, then the radius of the second sphere is

If two bodies of masses 2 kg and 3 kg are moving at right angles with velocities $20 \mathrm{~ms}^{-1}$ and $10 \mathrm{~ms}^{-1}$ respectively, then the velocity of the centre of mass of the system of the two bodies is

$5 \mathrm{~ms}^{-1}$

$30 \mathrm{~ms}^{-1}$

$10 \mathrm{~ms}^{-1}$

$14 \mathrm{~ms}^{-1}$

A particle of mass $8 \mu \mathrm{~g}$ in motion collides with another stationary particle of mass $4 \mu \mathrm{~g}$. If the collision is perfectly elastic and one dimensional, the ratio of their de-Broglie wavelengths after collision is

A soccer ball of mass 250 g is moving horizontally to the left with a speed $22 \mathrm{~ms}^{-1}$. This ball is kicked towards right with a velocity $30 \mathrm{~ms}^{-1}$ at an angle $53^{\circ}$ with the horizontal in upward direction. Assuming that it took 0.01 s for the collision to take place, the average force acting is $\left(\cos 53^{\circ}=\frac{3}{5}, \sin 53^{\circ}=\frac{4}{5}\right)$

A body of mass 30 kg moving with a velocity $20 \mathrm{~ms}^{-1}$ undergoes one-dimensional elastic collision with another ball of same mass moving in the opposite direction with a velocity of $30 \mathrm{~ms}^{-1}$. After collision the velocity of first and second bodies respectively are

$25 \mathrm{~ms}^{-1}, 30 \mathrm{~ms}^{-1}$

$30 \mathrm{~ms}^{-1}, 30 \mathrm{~ms}^{-1}$

$30 \mathrm{~ms}^{-1}, 20 \mathrm{~ms}^{-1}$

$40 \mathrm{~ms}^{-1}, 15 \mathrm{~ms}^{-1}$

Two blocks of equal masses are tied with a light string passing over a massless pulley (assuming frictionless surfaces ) acceleration of centre of mass of the two blocks is $\left(g=10 \mathrm{~ms}^{-2}\right)$

AP EAPCET 2024 - 22th May Evening Shift Physics - Center of Mass and Collision Question 15 English

$\frac{5(\sqrt{3}-1)}{2}$

$\frac{5(\sqrt{3}-1)}{2 \sqrt{2}}$

$\frac{5(\sqrt{3}+1)}{2 \sqrt{2}}$

$\frac{5(\sqrt{3}-1)}{\sqrt{2}}$

A ball falls freely from rest from a height of 6.25 m on a hard horizontal surface. If the ball reaches a heightd 81 cm after second bounce from the surface, the coefficient of restitution is

A body of mass 2 kg collides head on with another body of mass 4 kg . If the relative velocities of the bodies before and after collision are $10 \mathrm{~ms}^{-1}$ and $4 \mathrm{~ms}^{-1}$ respectively. The loss of kinetic energy of the system due to the collision is

A wooden plank of mass 90 kg and length 3.3 m is floating on still water. A girl of mass 20 kg walks from one end to the other end of the plank. The distance through which the plank moves is

A ball falls freely from rest on to a hard horizontal floor and repeatedly bounces. If the velocity of the ball just before the first bounce is $7 \mathrm{~ms}^{-1}$ and the coefficient of restitution is 0.75 , the total distance travelled by the ball before it comes to rest is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

Two blocks of masses $m$ and $2 m$ are connected by a massless string which passes over a fixed frictionless pulley. If the system of blocks is released from rest, the speed of the centre of mass of the system of two blocks after a time of 5.4 s is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

$18 \mathrm{~ms}^{-1}$

$8 \mathrm{~ms}^{-1}$

$4 \mathrm{~ms}^{-1}$

$12 \mathrm{~ms}^{-1}$

In an inclastic collision, after collision the kinetic energy

increases by 2 times

is less than before collision

is more than before collision

Ball $A$ of mass 1 kg moving along a straight line with a velocity of $4 \mathrm{~ms}^{-1}$ hits another ball $B$ of mass 3 kg which is at rest. After collision, they stick together and move with the same velocity along the same straight line. If the time of impact of the collision is 0.1 s then the force exerted on $B$ is

Two balls $A$ and $B$, of masses $M$ and $2 M$ respectively collide each other. If the ball $A$ moves with a speed of $150 \mathrm{~ms}^{-1}$ and collides with ball $B$, moving with speed $v$ in the opposite direction. After collision if ball $A$ comes to rest and the coefficient of restitution is 1 (one), then the speed of the ball $B$ before it collides with ball $A$ is

$37.5 \mathrm{~ms}^{-1}$

$12.5 \mathrm{~ms}^{-1}$

$75 \mathrm{~ms}^{-1}$

$25 \mathrm{~ms}^{-1}$

As shown in the figure, an iron block $A$ of volume $0.25 \mathrm{~m}^3$ is attached to a spring $S$ of unstretched length 1.0 m and hanging to the ceiling of a roof. The spring gets stretched by 0.2 m . This block is removed and another block $B$ of iron of volume $0.75 \mathrm{~m}^3$ is now attached to the same spring and kept on a frictionless incline plane of $30^{\circ}$ inclination. The distance of the block from the top along the incline at equilibrium is

AP EAPCET 2022 - 4th July Evening Shift Physics - Center of Mass and Collision Question 25 English

A ball of mass 0.5 kg moving horizontally at $10 \mathrm{~ms}^{-1}$ strikes a vertical wall and rebounds with speed $v$. The magnitude of the change in linear momentum is found to be $8.0 \mathrm{~kg}-\mathrm{~ms}^{-1}$. The magnitude of $v$ is

$6.0 \mathrm{~ms}^{-1}$

$9.0 \mathrm{~ms}^{-1}$

$26.0 \mathrm{~ms}^{-1}$

$13.0 \mathrm{~ms}^{-1}$

Masses $m\left(\frac{1}{3}\right)^N \frac{1}{N}$ are placed at $x=N$, when $N=2,3,4 \ldots \infty$. If the total mass of the system is $M$, then the centre of mass is

$\frac{1}{6} \frac{m}{M}$

$\frac{1}{5} \frac{m}{M}$

$\frac{1}{3} \frac{m}{M}$

$\frac{1}{2} \frac{m}{M}$

A ball of mass 3 kg, moving with a speed of 100 ms$^{-1}$, strikes a wall at an angle 60$^\circ$ (as shown in figure). The ball rebounds at the same speed and remains in contact with the wall for 0.2 s, the force exerted by the ball on the wall is

AP EAPCET 2021 - 20th August Evening Shift Physics - Center of Mass and Collision Question 28 English

A metal ball of mass 2 kg moving with a velocity of 36 km/h has a head on collision with a stationary ball of mass 3 kg. After the collision, if both balls move together, then the loss in kinetic energy due to collision is

A particle of mass m, moving with a velocity v makes an elastic collision in one dimension with a stationary particle of mass m. During the collision, they remain in contact with each other for an extremely small time T. Their force of contact, with time is shown in the figure. Then, F₀

AP EAPCET 2021 - 19th August Morning Shift Physics - Center of Mass and Collision Question 30 English

The sum of moments of all the particles in a system about its centre of mass is always