Question

The top in figure has a moment of inertia of $4.00\times {10}^{-4}kg-m^2$ and is initially at rest. It is free to rotate about the stationary axis $A{A}^{\prime }$ 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 $2.5M$ . If the string does not slip while it is unwound from the peg, what is the angular speed of the top after $80.0cm$ string has been pulled off the peg?

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

Answer 1

The correct option is D $100rad/s$

Since the force applied on the string is same as that of the tension in the string.

The work done is given as,

$W=F\times s$

$=2.5\times 80\times {10}^{-2}$

$=2J$

From the work energy rule it can be written as,

$W=\frac{1}{2}I{\omega }^2$

$2=\frac{1}{2}\times 4\times {10}^{-4}{\omega }^2$

$\omega =100rad/sec$

Thus, the angular speed is $100rad/sec$.