Question

A body is moving in a circular path with acceleration $a$. If its speed gets doubled, find the ratio of acceleration after and before the speed is changed

• A. $1:4$
• B. $1:2$
• C. $2:1$
• D. $4:1$

Answer 1

The correct option is D $4:1$

When an object moves in circular path with constant speed, then its acceleration is given by
$a=\frac{v^2}{R}$
Now, we have
$a_1=\frac{v^2}{R}$
When speed is doubled, acceleration is given by
$a_2=\frac{(2v{)}^2}{R}=\frac{4v^2}{R}$
Therefore, the ratio of final and initial accelerations will be
$\frac{a_2}{a_1}=\frac{4v^2/R}{v^2/R}=\frac{4}{1}$

Hence, option D is the correct answer.