Velocity of Separation and Approach

Q.

A large body of mass 100 kg moving with a velocity of 10.0 m/s collides elastically with a small body of mass 100 g at rest. The velocity of the small body is

1. 5 m/s

2. 10 m/s

3. 25 m/s

4. 20 m/s

Q. A particle of mass 100g moving at an initial spped u collides with another particle of same mass kept initially at rest. If the total kinetic energy becomes 0.5J after the collision, what could be the minimum and the maximum value of u.

1. 2 m/s, 4 m/s
2. 2 m/s, 2$\sqrt{2}$m/s
3. $2\sqrt{2}$m/s , 2 m/s
4. 2 m/s , 2 m/s

Q. A particle of mass $m$ is dropped from a height $h$ above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of $\sqrt{2gh}$ . If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of $\sqrt{\frac{h}{g}}$ is

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

Q. A small ball of mass $m$ is connected by an inextensible massless string of length $l$ with another ball of mass $M=4\text{m}$. They are released with zero tension in the string from a height $h$ as shown in the figure. The time after which string becomes taut for the first time after the release(after the mass $M$ collides with the ground ) is $\frac{l}{\sqrt{ngh}},$ where $n=$
(Assume all collisions to be elastic)

Q. Two equal mass objects are moving in a circular path with constant speed as shown in the figure. The collision is elastic everytime. They meet at $A$ again on $n^{th}$ collision, find the value of $n?$

[Assume, collisions are elastic in nature]

1. $1$
2. $2$
3. $3$
4. $4$

Q. A prticle of mass $m$ moves with velocity $v_0=20\text{m/s}$ towards a large wall that is moving with velocity $v=5\text{m/s}$ towards the particle as shown. If the particle collides with the wall elastically, then find the speed of the particle just after collision. (Assume collision with the wall is elastic)

1. $30\text{m/s}$
2. $20\text{m/s}$
3. $25\text{m/s}$
4. $22\text{m/s}$

Q. A small ball of mass $m$ is connected by an inextensible massless string of length $l$ with another ball of mass $M=4m$. They are released with zero tension in the string from a height $h$ as shown in the figure. The time $t$ after which the string becomes taut for the first time after the mass $m$ collides with the ground is (Assume all the collisions to be elastic)

1. $t=\frac{l}{\sqrt{gh}}$
2. $t=\frac{l}{\sqrt{3gh}}$
3. $t=\frac{l}{\sqrt{2gh}}$
4. $t=\frac{3l}{\sqrt{2gh}}$