A man of mass `100 kg` stands at the rim of a turtable of radius `2 m` and moment of inertia `4000 kgm^(2)` mounted on a vertical frictionless shaft at its centre. The whole system is initially at rest. The man now walks along the outer edge of the turntable with a velocity of `1m//s` relative to the earth
a. With what angular velocity and in what direction does the turntable rotate?
b. Through what angle will it have rotated when the man reaches his initial position on the turntable?
c. Through what angle will it have rotated when the man reaches his initial position relative to the earth?

Options

A. `pi/5 rad//sec`
B. `(2pi)/5 rad//sec`
C. `(2pi)/11 rad//sec`
D. `(pi)/11 rad//sec`

Answer

A

Explanation

if the man complete one revolution on the earth, then theta_(m)=2pi)`
time=(2pi)/(omega_(m))=(2pi)/0.5`
During this time, angular displacement on the table, `theta_(t)=omega_(t)`(time)=-0.05xx(2pi)/0.5`
`theta_(t)=-(pi)/5 radian, theta_(t)=36^(@)` in clockwise direction