Question

A thin spherical shell lying on a rough horizontal surface is hit by a cue in such a way that line of action passes through the centre of the shell. As a result shell starts moving with a linear speed v without any initial angular velocity. Find the linear velocity to the shell when it starts pure rolling.

• A. $\frac{3}{5}v$
• B. $\frac{2}{5}v$
• C. $\frac{4}{5}v$
• D. None

Answer 1

Answer: (A)

$\frac{3}{5}v$

Answer 2

v_f = v - $\frac{F_{f}}{m}t$ ……….. (i) F₁r = α

or F_fr = $\frac{2}{3}mr^{2}\alpha$

or α = $\frac{3}{2}\frac{F_{f}}{mr}\omega = 0 + \alpha t$

or ω = $\frac{3}{2}\frac{F_{f}}{mr}$t

or rω = v_f = $\frac{3F_{f}}{2m}$t ………. (ii)

From eq. (i) and (ii) v_f = $\frac{3}{5}v.$