Question

A car goes around uniform circular track of radius $R$ at a uniform speed $v$ once in every $T$ seconds. The magnitude of the centripetal acceleration is $a_C$. If the car now goes uniformly around a larger circular track of radius $2R$ and experiences a centripetal acceleration of magnitude $8a_c$, then its time period is

• A. $2T$
• B. $3T$
• C. $T/2$
• D. $3/2T$

Answer 1

The correct option is C $T/2$

$a_C=mR{\omega }^2=mR\ast 4{\pi }^2/T^2$

$8a_C=m2R\ast 4{\pi }^2/T^{\prime 2}$

Dividing,

$8=\left(2/T^{\prime 2}\right)\ast \left(T^2/1\right)=2T^2/T^{\prime 2}$

$T^{\prime }=\sqrt{T^2/4}=T/2$

So option C is correct.