A uniform solid sphere having mass M is placed on a smooth horizontal surface. A sudden blow is given horizontally to the sphere at a height h = 4 R /5 above the centre line. Find the minimum time (in

Question

A uniform solid sphere having mass M is placed on a smooth horizontal surface. A sudden blow is given horizontally to the sphere at a height $h = 4 R /5$ above the centre line. Find the minimum time (in sec) after which the highest point B will touch the ground. I is the impulse of the blow. (Given: I = 4 N-s, M = 2 kg, $R = \frac{4}{π}$ m)

TestHub · Accepted Answer

Linear impulse gives translation only

Angular impulse about the centre:

$I h = \frac{2}{5} M R^{2} ω$

$ω = \frac{5 I h}{2 M R ^{2}} = \frac{5 \times 4 \times ( 4 R /5 )}{2 \times 2 \times R ^{2}} = \frac{4}{R} = π rad/s$

B reaches the ground after half a turn

$t = \frac{π}{ω} = 1 s$

Answer: 1

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