A boy of mass 30kg is running with a velocity of 3 ms^-1 on ground just tangentially to a merry - go -round which is at rest. It has radius R = 2m, a masses of 120 kg and its radius of gyration is 1m. If the boy suddenly jumps on to the merry -go - round, the angular velocity acquired by the system is

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3/4 rad s^–1

0.5 rad s^–1

4/3 rad s^–1

1 rad s^–1

answer is C.

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Detailed Solution

From Law of conservation of angular momentum :

$\Rightarrow$ L_i = L_f

$\Rightarrow mvR = ({mR}^{2} + {Mk}^{2}) ω$

$ω = \frac{(30) (3) (2)}{(30) {(2)}^{2} + (120) {(1)}^{2}} = \frac{3}{4} rad / \sec$

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