Question

In a figure shown, the two identical balls of mass M and radius R each, are placed in contact with each other on the frictionless horizontal surface. The third ball of mass M and radius R/2, is coming down vertically and has a velocity= $v_0$ when it simultaneously hits the two balls and itself comes to rest. Then, each of the two bigger balls will move after collision with a speed equal to

• A. $\frac{4v_0}{\sqrt{5}}$
• B. $\frac{2v_0}{\sqrt{5}}$
• C. $\frac{v_0}{\sqrt{5}}$
• D. None

Answer 1

The correct option is C $\frac{v_0}{\sqrt{5}}$

From thew figure,

$Fdtcos\theta =Mv$ .............(1)

$-Fdtsin\theta =0-M{v}_0$

$Fdtsin\theta =M{v}_0$ .........(2)

From equation (1) and (2),

$tan\theta =\frac{v_0}{v}$ ..........(3)

From $△AOC$

$tan\theta =\frac{\sqrt{5}R/2}{R/2}=\sqrt{5}$

$\sqrt{5}=\frac{v_0}{v}$

$v=\frac{v_0}{\sqrt{5}}$