A disc of mass m and radius R lies flat on a smooth horizontal table. A particle of mass m, moving horizontally along the table, strikes the disc with velocity V while moving along a line at a distance $\frac{R}{2}$ from the centre. Find the angular velocity acquired by the disc if the particle comes to rest after the impact

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$\frac{v}{4 R}$

$\frac{3 v}{4 R}$

$\frac{v}{2 R}$

$\frac{v}{R}$

answer is C.

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Detailed Solution

Impulse to the particle $= mV (⟵)$

Impulse to the disc $= mV (\to)$

Angular impulse about centre $= mV \frac{R}{2}$
$∴ \frac{1}{2} {mR}^{2} . ω = mV \frac{R}{2} ∴ ω = \frac{V}{R}$

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