Two masses P and Q connected with an ideal string of length L lie on a smooth horizontal plane. Q is given a velocity V along the ground perpendicular to line PQ (see figure). Find the tension in the string during their subsequent motion.

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

$\frac{m v^{2}}{L}$

$\frac{8}{5} . \frac{m v^{2}}{L}$

$\frac{3 m v^{2}}{L}$

$\frac{6}{5} . \frac{m v^{2}}{L}$

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

In COM reference frame, particles P and Q move along circular path with same angular velocity $(ω)$
$Y_{C O M} = \frac{(3 m \times 0) + (2 m) L}{3 m + 2 m} = \frac{2}{5} L$
$V_{C O M} = \frac{(3 m \times V) + (2 m \times 0)}{3 m + 2 m} = \frac{3}{5} V$
In COM frame velocity of 3n mass= $v - \frac{3}{5} v = \frac{2}{5} v$
Angular velocity of 3m mass is
$ω = \frac{(2 / 5) V}{(2 / 5) L} = \frac{V}{L}$
$T = (3 m) ω^{2} r = (3 m) \frac{v^{2}}{L^{2}} . \frac{2}{5} L = \frac{6 m v^{2}}{5 L}$