Question

A sphere of mass m moving with a constant velocity collides with another stationary sphere of same mass. The ratio of velocities of two spheres after collision will be, if the co-efficient of restitution is e:

• A. $\frac{1-e}{1+e}$
• B. $\frac{e-1}{e+1}$
• C. $\frac{1+e}{1-e}$
• D. $\frac{e+1}{e-1}$

Answer 1

The correct option is A $\frac{1-e}{1+e}$

The law of conservation of linear momentum tells us that the overall momentum before the collision must be equal to the overall momentum after a collision.

Since the spheres have identical masses, we can write

$mu+m\times 0=m{v}_A+m{v}_B$

$u=v_A+v_B$

From the definition of the coefficient of restitution, we know that

$e=\frac{v_B-v_A}{u}$

solving above two equations

$e\times (v_A+v_B)=v_B-v_A$

$v_B(1-e)=v_A(1+e)$

$\frac{v_A}{v_B}=\frac{1-e}{1+e}$