Question

If velocity of C immediately after collision becomes $v_0/2$ in the initial direction of motion, the impulse due to string on sphere A is :

• A. $\frac{m{v}_0}{8}$
• B. $\frac{m{v}_0}{2}$
• C. $\frac{\sqrt{m{v}_0}}{4}$
• D. none of these

Answer 1

The correct option is A $\frac{m{v}_0}{8}$

The velocity of C becomes $\frac{v_o}{2}$ & ball B sticks to ball C as it is a head-on inelastic collision.

$I=$ Impulse on A due to string

$=F\times t$

$I=m^{\prime }\times a\times t=m\times \left(\frac{v-u}{t}\right)\times t$

Where, $m^{\prime }=resultantmass=\frac{m^2}{m+m}$

$m^{\prime }=reducedmass=\frac{m}{2}$

$J=\frac{m}{2}\left(\frac{v_o-\frac{v_o}{2}}{2}\right)=\frac{m{v}_o}{8}$