Question

The sphere shown in figure lies on a rough plane when a particle of mass m travelling at a speed v0 collides and sticks with it. If the line of motion of the particle is at a distance h above the plane, find the linear speed of the combined system just after the collision. Assume that the mass M of the sphere is large compared to the mass of the particle so that the centre of mass of the combined system is not appreciably shifted from the centre of the sphere.

• A. $\frac{2m{v}_0}{M+m}$
• B. $\frac{M{v}_0}{M+m}$
• C. $V_0$
• D. $\frac{m{v}_0}{M+m}$

Answer 1

The correct option is D

$\frac{m{v}_0}{M+m}$

Take the particle plus the sphere as the system. Using conservation of linear momentum, the linear speed of the combined system v is given by

$m{v}_0=(M+m)vor,v=\frac{m{v}_0}{M+m}$. .....(i)