Question

A strip of wood mass `M` and length `l` is placed on a smooth horizontal surface. An insect of mass `m` starts from rest at one end of the strip and walks to the other end in time `t`, moving with a constant speed.
A. The speed of the insect as seen from the ground is `lt (l)/(t)`.
B. The speed of the spring as seen from the ground is `(l)/(t)((M)/(M+m))`
C. The speed of the strip as seen from the ground is `(l)/(t)((m)/(M+m))`
D. The total kinetic energy of the system is `(1)/(2)(m+M)((l)/(t))^(2)`.

Answer 1

Correct Answer - A::C
`mv_(1) = Mv_(2)`, where `v_(1)` and `v_(2)` are speeds of mass `m` and `M`, as seen from ground. The velocity of `m` relative to `M` is `v_(12) = v_(1)-(-v_(2))`.

Hence, `t = (1)/(v_(12)) =(1)/(v_(1)+v_(2))` or `v_(1)+v_(2) = l//t`.