Velocity of Separation and Approach

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

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. 20 m/s

2. 5 m/s

3. 10 m/s

4. 25 m/s

Q. A particle is projected with a speed $u$ at an angle $\theta$ with horizontal from point $A$. It strikes elastically with a vertical wall at height $h/2$. It rebounds and reaches maximum height $h$ and falls back on the ground at point $B$ as shown in Figure. Distances from $A$ to wall and from wall to $B$ are $x_1$ and $x_2$, and time to cover is $t_1$ and $t_2$ respectively. Match the values in column I with the expressions in column II.


$$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{i.}\sqrt{2}& \text{a.}\frac{x_2-x_1}{x_2+x_1}\text{or}\frac{x_2+x_1}{x_2-x_1}\\ \text{ii.}\frac{1}{\sqrt{2}}& \text{b.}\frac{t_2-t_1}{t_2+t_1}\text{or}\frac{t_2+t_1}{t_2-t_1}\\ \text{iii.}1& \text{c.}\frac{u\sin \theta }{g(t_2+t_1)}\\ \text{iv.}\frac{1}{2}& \text{d.}\frac{u\cos \theta (t_1+t_2)}{x_1+x_2}\end{array}$$

1. $\text{(i) a, b (ii) a, b (iii) d (iv) c}$
2. $\text{(i) a (ii) b (iii) d (iv) c}$
3. $\text{(i) a, b (ii) a, b (iii) d (iv) c}$
4. $\text{(i) a (ii) a, c (iii) d (iv) b}$

Q. Two equal mass objects are moving in a circular path with constant speed as shown in figure. After how many collisions they will again meet at $A$.

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

Q. A ball of mass $m$ moving with speed $u$ undergoes a head on perfect elastic collision with mass $nm$ initially at rest. The fraction of the energy transferred to the second ball by the first ball is

1. $\frac{n}{(1+n)}$
2. $\frac{n}{(1+n{)}^2}$
3. $\frac{2n}{(1+n{)}^2}$
4. $\frac{4n}{(1+n{)}^2}$

Q. A ball moving at a speed of $3\text{m/s}$ approaches a wall moving towards it with a speed of $3\text{m/s}$. After the perfectly elastic collision, the speed of the ball will be

1. $3\text{m/s}$
2. $6\text{m/s}$
3. $9\text{m/s}$
4. $0$

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

Q. A smooth sphere of mass $M$ moving with velocity $u$ directly collides elastically with another sphere of mass $m$ at rest. After the collision, their final velocities are $V$ and $v$ respectively. The value of $v$ is:

1. $\frac{2uM}{m}$
2. $\frac{2um}{M}$
3. $\frac{2u}{1+\frac{m}{M}}$
4. $\frac{2u}{1+\frac{M}{m}}$

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. There is formation of layer of snow x cm thick on water, when the temperature of air is $-{\theta }^{o}C$ (less than freezing point). The thickness of layer increases from x to y in the time t, then the value of t is given by

1. 

2. 

3. 

4.