Question

A turn table is rotating in horizontal plane about its own axis at an angular velocity $90rpm$ while a person is on the turn table at its edge. If he gently walks to the centre of table by which moment of inertia of system decreases by $25\%$, then the time period of rotation of turn table is:

• A. $0.5s$
• B. $1s$
• C. $1.5s$
• D. $2s$

Answer 1

Answer: (A)

$0.5s$

Let the initial MI be $I$ and final will be $0.75I$

Using angular momentum conservation

$I\times N=I_1\times N_1$

$I\times 90=0.75I{N}_1\Rightarrow N_1=120rpm$

So ${\omega }_1=2\pi \times 120/2=4\pi$

$T=2\pi /{\omega }_1=0.5s$