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(B) The minimum velocity required at the lowest point to complete a vertical circular motion is given by the formula $v = \sqrt{5gr}$,where $g$ is the

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$v/2$

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(B) The minimum velocity required at the lowest point to complete a vertical circular motion is given by the formula $v = \sqrt{5gr}$,where $g$ is the acceleration due to gravity and $r$ is the length of the string.From this relation,we can see that $v \propto \sqrt{r}$.Let the initial length be $r_1 = r$ and the initial velocity be $v_1 = v$.Let the new length be $r_2 = r/4$ and the new velocity be $v_2$.Using the proportionality $v_2 / v_1 = \sqrt{r_2 / r_1}$,we get:$v_2 / v = \sqrt{(r/4) / r} = \sqrt{1/4} = 1/2$.Therefore,the new velocity is $v_2 = v/2$.

The minimum velocity $v$ required for a simple pendulum to complete one full rotation in a vertical plane is given. If the length of the string is reduced to one-fourth,what will be the new required velocity?

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