Question

A stone is attached at the end of a string and rotated in a horizontal circle by a student. If the final speed of the stone is $2$ times the initial speed, then the final centripetal force is $x$ times the initial centripetal force. The value of $x$ is:

• A. $2$
• B. $4$
• C. $\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

The correct option is B $4$

Given, final speed of stone
$v_f=2\times v_i$ (intial speed)

Then, final centripetal force
$F_{final}=\frac{m{v}_f^2}{r}=4\times \frac{m{v}_i^2}{r}=4F_{initial}$
where $F_{initial}$ is the initial centripetal force.
$\therefore x=4$