A body is moving in a circular path with acceleration a. If its velocity gets doubled, then the ratio of acceleration after and before the change is

Question

A body is moving in a circular path with acceleration a. If its velocity gets doubled, then the ratio of acceleration after and before the change is (A) 1: 4 (B) (1/4): 1 (C) 2: 1 (D) 4: 1

Tardigrade Admin · Accepted Answer

Centripetal acceleration, a=(v2/r) i.e., a propto v2 ∴ (a2/a1)=(v22/v12)=((2 v)2/(v)2)=4

Q. A body is moving in a circular path with acceleration $a$ . If its velocity gets doubled, then the ratio of acceleration after and before the change is

$1 : 4$

$\frac{1}{4} : 1$

$2 : 1$

$4 : 1$

Centripetal acceleration, $a = \frac{v ^{2}}{r}$ i.e., $a \propto v^{2}$
$∴ \frac{a _{2}}{a _{1}} = \frac{v _{2}^{2}}{v _{1}^{2}} = \frac{( 2 v ) ^{2}}{( v ) ^{2}} = 4$

Q. A body is moving in a circular path with acceleration a. If its velocity gets doubled, then the ratio of acceleration after and before the change is

1:4

41​:1

2:1

4:1