Question

Refer to a ball of mass $m$ on a string of length $R$, swinging around in circular motion, with instantaneous velocity $v$ and centripetal acceleration $a$. What is the centripetal acceleration of the ball if the length of the string is doubled?

• A. $\frac{a}{4}$
• B. $\frac{a}{2}$
  
• C. $a$
  
• D. $2a$
  
• E. $4a$
  

Answer 1

Answer: (B)

$\frac{a}{2}$

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

New length of the string $R^{\prime }=2R$

Thus new centripetal acceleration $a^{\prime }=\frac{v^2}{R^{\prime }}=\frac{v^2}{2R}=\frac{a}{2}$