2D Collision Example

Q.

In the figure shown below, two identical balls of mass $M$ and radius $R$ each, are placed in contact with each other on the frictionless horizontal surface. The third ball of mass $M$ and radius $R/2$, is coming down vertically and has a velocity $v_0$ when it hits the two balls symmetrically and itself comes to rest. Then, each of the two bigger balls will move after collision with a speed equal to

1. $\frac{4v_0}{\sqrt{5}}$
2. $\frac{2v_0}{\sqrt{5}}$
3. $\frac{v_0}{\sqrt{5}}$
4. $\sqrt{5}{v}_0$

Q.

A hunter aims his gun and fires a bullet directly at a monkey on a tree. At the instant the bullet leaves the barrel of the gun, the monkey drops. Will the bullet hit the monkey? Substantiate (give proper evidence to prove the truth of) your answer with proper reasoning.

Q.

The track shown in figure (9-E16) is frictionless. The block B of mass 2m is lying at rest and the block A of mass m is pushed along the track with some speed. the collision between A and B is perfectly elastic. With what velocity should the block A be started to get the sleeping man awakened ?

Q. A particle is projected from ground with speed $u$ such that the horizontal range is $R$ and maximum height is $H$. The angular velocity of the particle about the point of projection, when it is at the highest point of its trajectory is:

1. $\frac{HRu}{(R^2+4H^2)\sqrt{R^2+16H^2}}$
2. $\frac{4HRu}{(R^2+4H^2)\sqrt{R^2+16H^2}}$
3. $\frac{u}{H}$
4. $\frac{uR}{\left(H\right)\sqrt{R^2+16H^2}}$

Q.

A ball collides elastically with another ball of the same mass. The collision is oblique and initially second ball was at rest. After the collision, the two balls move with same speeds. What will be the angle between the velocities of the balls after the collision?

1. 

2. 

3. 

4. 

Q. A ball of mass 'm' moving with a velocity 'v' undergoes an oblique elastic collision with another ball of the same mass 'm' but at rest. After the collision, if the two balls move with different speeds after the collision, the angle between their directions of motion will be

1. Less than
2. More than
3. Exactly
4. Exactly

Q. A plank of mass $5\text{kg}$ is placed on a frictionless horizontal plane. Further a block of mass $1\text{kg}$ is placed over the plank. A massless spring of natural length $2\text{m}$ is fixed to the plank by its one end. The other end of spring is compressed by the block by half of spring's natural length. The system is now released from the rest, velocity of the plank when block leaves the plank is

[Assume, there is no friction between the two blocks]

1. $\sqrt{\frac{5}{3}}\text{m/s}$
2. $\sqrt{\frac{7}{3}}\text{m/s}$
3. $\sqrt{\frac{8}{3}}\text{m/s}$
4. $\sqrt{\frac{10}{3}}\text{m/s}$

Q. A smooth sphere of mass $m=5\text{kg}$ is moving on a horizontal plane with a velocity $(5\hat{i}+\hat{j})\text{m/s}$ when it collides with a vertical wall which is parallel to the vector $\hat{j}.$ If the coefficient of restitution between the sphere and the wall is $\frac{1}{2}$, find the loss in kinetic energy caused by the impact.

1. $32.5\text{J}$
2. $46.875\text{J}$
3. $49.375\text{J}$
4. $0\text{J}$

Q.

In an ……. collision, the kinetic energy before collision is equal to the kinetic energy after collision.

Q. A sphere of mass $M=2\text{kg}$ moving with a velocity of $2\sqrt{2}\text{m/s}$ collides with another sphere of mass $m=1\text{kg}$ initially at rest at an angle of ${45}^{\circ }$ with the horizontal. If the coefficient of restitution of the collision is 0.5, what will be the final velocity(in $\text{m/s}$) of the sphere having mass $m$ ?

1. $-\sqrt{2}\hat{i}+\sqrt{2}\hat{j}$
2. $\sqrt{2}\hat{i}-\sqrt{2}\hat{j}$
3. $\sqrt{2}\hat{i}+\sqrt{2}\hat{j}$
4. $-\sqrt{2}\hat{i}-\sqrt{2}\hat{j}$

Q. A projectile is launched with a speed of 10 m/s at an angle ${60}^{\circ }$ with the horizontal from a sloping surface of inclination ${30}^{\circ }$. The range R is $(Takeg=10m/s^2)$

1. 4.9 m
2. 13.3 m
3. 9.1 m
4. 12.6 m

Q. a particle is thrown with an initial velocity of v= ai+bj , if the range of projectile is double of the maximum height reached by it then what is the relation between a and b? n nti along x axis and j along y axis

Q. Two particles are projected from the same point, with the same speed $u$ such that they have the same range $R$, but different maximum heights $h_1\text{and}{h}_2$. Which of the following is correct ?

1. $R^2=2h_1{h}_2$
2. $R^2=h_1{h}_2$
3. $R^2=16h_1{h}_2$
4. $R^2=4h_1{h}_2$

Q. A ball is projected with a speed of $2m{s}^{-1}$ with respect to a trolley which is moving with $4m{s}^{-1}$ as shown. The angle at Which ball is proejcted with respect to the horizontal in ground frame is

diagram

1. ${\tan }^{-1}\left(\frac{5}{\sqrt{3}}\right)$
2. ${\sin }^{-1}\left(\frac{5}{\sqrt{28}}\right)$
3. ${\tan }^{-1}\left(\sqrt{\frac{3}{28}}\right)$
4. ${\sin }^{-1}\left(\sqrt{\frac{3}{28}}\right)$

Q. The block shown in figure is released from rest when the extension in spring (of spring constant $k$) is $2\text{m}$. Find out the speed of the block when the spring is compressed by $1\text{m}$.

1. $\sqrt{\frac{k}{2}}$
   
2. $\sqrt{\frac{3k}{2}}$
   
3. $\sqrt{\frac{5k}{2}}$
   
4. $\sqrt{\frac{7k}{2}}$
   

Q.

A projectile is thrown with a velocity vat an angle a with horizontal. When the projectile is at a height equal to half of the maximum height, the vertical component of the velocity of projectile is

1. v sin a * 3
2. vsin a / 3
3. vsin a / root 2

Q. A ball is thrown at a triangular wedge with an angle of inclination ${60}^o$ parallel to the ground as shown in the figure. After bouncing against the wedge, the velocity of the ball is perpendicular to the ground. What is the coefficient of restitution?

1. $1$
2. $\frac{1}{6}$
3. $\frac{1}{3}$
4. $\frac{1}{\sqrt{3}}$

Q. A smooth sphere of mass $m=5\text{kg}$ is moving on a horizontal plane with a velocity $(5\hat{i}+\hat{j})\text{m/s}$ when it collides with a vertical wall which is parallel to the vector $\hat{j}.$ If the coefficient of restitution between the sphere and the wall is $\frac{1}{2}$, find the loss in kinetic energy caused by the impact.

1. $46.875\text{J}$
2. $0\text{J}$
3. $32.5\text{J}$
4. $49.375\text{J}$

Q. Trajectory of two particles projected from origin with speeds $v_1$ and $v_2$ at angles ${\theta }_1$ and ${\theta }_2$ with positive x-axis respectively are as shown in the figure. Given that $g=-10{\text{m/s}}^2\left(\hat{j}\right)$. Choose the correct option(s) related to diagram.

1. $v_1-v_2=2v_1$
2. ${\theta }_2-{\theta }_1=2{\theta }_1$
3. $v_1=v_2$
4. $3({\theta }_2-{\theta }_1)=+{\theta }_1$

Q. Which of the following quantities remains constant in a collision?

1. Kinetic energy
2. Momentum
3. Temperature
4. Both (a) and (b)

Q. Two balls are colliding obliquely. Assume that the balls are smooth and all other external forces are absent then,

1. The component of the momentum of system perpendicular to the line of impact is conserved.
2. The component of the momentum of each ball separately perpendicular to the line of impact is conserved.
3. Both (a) and (b) are correct.
4. Both (a) and (b) are incorrect.

Q. Which of the following statements is correct for an inelastic collision?

1. The kinetic energy of each body remains constant.
2. The initial kinetic energy is greater than the final kinetic energy.
3. The initial kinetic energy is equal to the final kinetic energy.
4. The initial kinetic energy is less than the final kinetic energy.

Q. Blocks A and B are at rest with the spring at its natural length and block C collides elastically with A. Then,

1. The kinetic energy of the A - B system at maximum compression of the spring is zero.
2. The kinetic energy of the A - B system at maximum compression of the spring is $100\text{J}$.
3. The maximum compression of the spring is $1.5\text{m}$.
4. The maximum compression of the spring is $1\text{m}$.

Q. A ball of mass 20 kg moving at 2 m/s horizontally strikes another ball of mass 12 kg at rest. If after the collision, the 20 kg ball is now moving with a velocity of 1 m/s at an angle of 30° with the horizontal. Find the final velocity of the 12 kg ball.

1. 2.54 i + 1.62 j
2. 2.54 i - 1.62 j
3. 1.89 i + 0.83 j
4. 1.89 i - 0.83 j

Q. ntA grenade having mass of 10kg flying horizontally with a velocity 0f 10m/s explodes into two fragments .the larger fragment has a velocity 25 m/s in the direction of initial velocity of grenade the smaller fragment has a velocity of 12.5 m/s in the opposite direction .The masses of fragments are ?n

Q. An ideal massless spring $S$ can be compressed $1\text{m}$ by a force of $100\text{N}$ in equilibrium. The same spring is placed at the bottom of a frictionless inclined plane incline at ${30}^{\circ }$ to the horizontal. A block $M$ of mass $10\text{kg}$ is released from rest at the top of the plane and is brought to rest momentarily after compressing the spring by $2\text{m}$. If $g=10{\text{m/s}}^2$, what is the speed of mass just before it touches the spring ?

1. $\sqrt{20}\text{m/s}$
2. $\sqrt{30}\text{m/s}$
3. $\sqrt{10}\text{m/s}$
4. $\sqrt{40}\text{m/s}$

Q. A ball of mass 20 kg moving at 2 m/s horizontally strikes another ball of mass 12 kg at rest. If after the collision, the 20 kg ball is now moving with a velocity of 1 m/s at an angle of 30° with the horizontal. Find the final velocity of the 12 kg ball.

1. 2.54 i + 1.62 j
2. 2.54 i - 1.62 j
3. 1.89 i + 0.83 j
4. 1.89 i - 0.83 j

Q. Two putty balls of equal masses moving with equal speeds in mutually perpendicular direction, stick together after collision. If the balls were initially moving with a speed of $45\sqrt{2}m{s}^{-1}$ each, the speed of their combined mass after collision is.

1. $45\sqrt{2}m{s}^{-1}$
2. $45m{s}^{-1}$
3. $90m{s}^{-1}$
4. $22.5\sqrt{2}m{s}^{-1}$

Q. A small object of uniform density rolls up a curved surface with in a initial velocity $v.$ It reaches up to a maximum height of $\frac{3v^2}{4g}$ with respect to the initial position. The object is-

1. Disc
2. Ring
3. Solid sphere
4. Hollow sphere

Q. Two bullets are fired horizontally with different velocities from the same height. Which will match the ground first?

1. Faster one
2. Both will reach simultaneously
3. Cannot be predicted
4. Slower one