Two point masses of mass m and 2m placed on smooth horizontal plane are connected by a light rod of length l. Masses are given velocities in horizontal plane perpendicular to rod as shown. If area of cross section of rod is A and Young's modulus is Y, then elongation in the rod, will be

Options

A. `(mv_(0)^(2))/(AY)`
B. `(2mv_(0)^(2))/(AY)`
C. `(6mv_(0)^(2))/(AY)`
D. `(3mv_(0)^(2))/(AY)`

Answer

C

Explanation

`T/(2m) + T/m = ((3v_(0))^(2))/(l)`
`T = (6mv_(0)^(2))/(l)`
`Y = ((6mv_(0)^(2))/(l))/(Delta l//Y) implies Delta l = (6mv_(0)^(2))/(AY)`.