Question

The top in figure has a moment of inertia of $4.00\times$ $10^{-4}kg\cdot m^2$ 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 $2.5N$. If the string does not slip while it is unwound from the peg, what is the angular speed of the top after $80.0cm$ of string has been pulled off the peg?

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

Answer 1

Answer: (D)

For the non-isolated system of the top,
$\Rightarrow W=\Delta K\Rightarrow F\Delta x=\left(\frac{1}{2}I{\omega }^2-0\right)$
$\omega =\sqrt{\frac{2F\Delta x}{I}}=\sqrt{\frac{2(2.5N)(0.800m)}{4\times 10^{-4}kg\cdot m^2}}=100rad/s$