Question

A ball rotating in a horizontal circle and tied to a string is connected to a mass m hanging vertically as shown in the figure. The mass is at rest when the radius is $r$ and speed of the ball is $v$. If the radius is reduced to $r/2$ such that the mass is still at rest, the new speed of the ball is given by:

• A. $\frac{1}{\sqrt{2}}v$
• B. $2v$
• C. $3v$
• D. $4v$
• E. $v$ (unchanged)

Answer 1

Answer: (A)

$\frac{1}{\sqrt{2}}v$

Given : $r_1=r$ $v_1=v$ $r_2=\frac{r}{2}$

As the mass is at rest initially and finally, thus the tension in the string remains the same.

Let mass of the ball be $m$.

$⟹$ $\frac{m{v}_1^2}{r_1}=\frac{m{v}_2^2}{r_2}$

OR $\frac{m{v}^2}{r}=\frac{m{v}_2^2}{r/2}$ $⟹v_2=\frac{v}{\sqrt{2}}$