Question

Two small identical spheres each of mass $m$ are projected slant-wise from the points $A$ and $B$ on the ground with equal velocities $u$ and making same angles $\theta$ and $\theta$ as shown in the figure. They collide with each other at the highest point $C$ of the common path. If the collision is completely inelastic, how much time after the collision the particles come back to the ground?

• A. $\frac{4usin\theta }{g}$
• B. $\frac{3usin\theta }{g}$
• C. $\frac{2usin\theta }{g}$
• D. $\frac{usin\theta }{g}$

Answer 1

The correct option is D $\frac{usin\theta }{g}$

At the highest point, the velocity of the masses will only be horizontal and will be equal to $u\cos \theta$.

After the masses stick together, the common velocity will be given as

$v=\frac{mu\cos \theta -mu\cos \theta }{m+m}=0$

So the body will be in free fall starting from rest.

For the vertical motion:

$\frac{1}{2}g{t}^2=H_{max}=\frac{u^2{\sin }^2\theta }{2g}$

Solving this, we get $t=\frac{u\sin \theta }{g}$