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(B) The centripetal acceleration $a_c$ of a body in uniform circular motion is given by the formula $a_c = \omega^2 R$,where $\omega$ is the angular v

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$2$

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(B) The centripetal acceleration $a_c$ of a body in uniform circular motion is given by the formula $a_c = \omega^2 R$,where $\omega$ is the angular velocity and $R$ is the radius.We know that angular velocity $\omega = 2 \pi n$,where $n$ is the frequency.Substituting this into the formula for centripetal acceleration:$a_c = (2 \pi n)^2 R$$a_c = 4 \pi^2 n^2 R$We are asked to find the centripetal acceleration per unit radius,which is $\frac{a_c}{R}$.$\frac{a_c}{R} = 4 \pi^2 n^2$Comparing this expression with $(n)^x$,we can see that the term is proportional to $n^2$.Therefore,the value of $x$ is $2$.

$A$ body performing uniform circular motion of radius '$R$' has frequency '$n$'. Its centripetal acceleration per unit radius is proportional to $(n)^x$. The value of $x$ is

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