The top in figure has a moment of inertia of `4.00 xx 10^-4 kg.m^2` and is initially at rest. It is free to rotate about the stationary axis `AA'`. A string, wrapped around a peg along the axis of the top, is pulled in such a manner as to maintain a constant tension of `2.5 N`.If the string does not slip while it is unwound from the peg. What the angular speed of the top after `80.0 cm` of string has been pulled off the peg ?
.

Options

A. `75 rad//s`
B. `50 rad//s`
C. `125 rad//s`
D. `100 rad//s`

Answer

D

Explanation

(d) For the non-isolated system of the top,
`rArr W = Delta K rArr F Deltax = ((1)/(2) I omega^2 - 0)`
`omega = sqrt((2 F Deltax)/(I)) = sqrt(2(2.5 N)(0.800 m))/(4 xx 10^-4 kg.m^2) = 100 rad//s`.