JEE Main · 2012 · 29 Apr 2012 · Offline · Kinematics

Two cars of masses

m_{1}

and

m_{2}

are moving in circles of radii

r_{1}

and

r_{2}

, respectively. Their speeds are such that they make complete circles in the same time

t

. The ratio of their centripetal acceleration is

(A) $m_{1} r_{1} : m_{2} r_{2}$
(B) $m_{1} : m_{2}$
(C) $r_{1} : r_{2}$ ✓ Correct
(D) $1 : 1$

Answer: (C)

Solution

Completing their circles in the same time, the two cars share the same angular speed

ω = \frac{2 π}{t}

. Centripetal acceleration is

a = ω^{2} r

, so

a_{1} = ω^{2} r_{1}

and

a_{2} = ω^{2} r_{2}

; the masses never enter. The ratio is

\frac{a _{1}}{a _{2}} = \frac{r _{1}}{r _{2}}

, that is

r_{1} : r_{2}

JEE Main · 2012 · 29 Apr 2012 · Offline · Single correct option

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