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

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)  (a/4)  (D)  (a/2)

Tardigrade Admin · Accepted Answer

The centripetal acceleration a=(v2/R) or a propto v2 or (a1/a2)=(v12/v22) =(a/a2)=(v2/(2 v)2)=(1/4) or a2=4 a

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

$4 a$

$2 a$

$\frac{a}{4}$

$\frac{a}{2}$

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 $a_{2} = 4 a$

Q. 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

4a

2a

4a​

2a​