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

Answer is : (c) T/2

When car goes around track of radius R, then

Time period, T = 2πR/v

Centripetal acceleration, a_c = v²/R

When car goes around circular track of radius 2R, then

Centripetal acceleration,

So, time period of car is