Question

A ball of mass $m$ is attached with the string of length $R$, rotating in circular motion, with instantaneous velocity $v$ and centripetal acceleration $a$.

Calculate the centripetal acceleration of the ball if the length of the string is doubled?

• A. $a/4$
• B. $a/2$
• C. $a$
• D. $2a$
• E. $4a$

Answer 1

Answer: (B)

$a/2$

Centripetal acceleration $a=\frac{v^2}{R}$

Now the length of the string is doubled keeping the instantaneous velocity constant i.e $R^{\prime }=2R$

$\therefore$ New centripetal acceleration $a^{\prime }=\frac{v^2}{R^{\prime }}=\frac{v^2}{2R}=\frac{a}{2}$