Question

A body moving along a circular path of radius $R$ with velocity $v$, has centripetal acceleration a. If its velocity is made equal to $2v$, then its centripetal acceleration is

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

Answer 1

Answer: (A)

$4\,a$

Answer 2

The centripetal acceleration $a=\frac{v^{2}}{R}$
or $a \propto v^{2}$
or $\frac{a_{1}}{a_{2}}=\frac{v_{1}^{2}}{v_{2}^{2}}$
$=\frac{a}{a_{2}}=\frac{v^{2}}{(2 v)^{2}}=\frac{1}{4}$
or $a_{2}=4\, a$