Question

A dense particle is rotating with uniform speed along a circle in horizontal plane with help of horizontal light string on smooth table surface. If the radius of circle is decreased by ${\frac{1}{3}}^{rd}$ of initial radius, the $\%$ change in the angular velocity of particle is :

• A. Increases by $50\%$
• B. Decreases by $50\%$
• C. Increases by $125\%$
• D. Decreases by $125\%$

Answer 1

Answer: (C)

Increases by $125\%$

Let the initial radius be R and angular velocity =$\omega$

Since angular momentum is conserved about axis of rotation

So $m{R}^2\omega =m(2R/3{)}^2{\omega }_1$

So ${\omega }_1=\frac{9\omega }{4}=2.25\omega$

So change =$\frac{{\omega }_1-\omega }{\omega }\times 100=125$%