A strip of wood of mass M and length $l$ is placed on a smooth horizontal surface. An insect of mass m starts at one end on the strip walks to the other end in time t, moving with a constant speed.

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The speed of the insect as seen from the ground is $< \frac{l}{t}$

The speed of the strip as seen from the ground is $\frac{l}{t} (\frac{M}{M + m})$

The speed of the strip as seen from the ground is $\frac{l}{t} (\frac{m}{M + m})$

The total kinetic energy of the system is $\frac{1}{2} (m + M) {(\frac{l}{t})}^{2}$

answer is A, C.

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Detailed Solution

Velocity of insect w.r.t strip $= \frac{l}{t}$
Let strip moves with speed v
Intial momentum was 0
$\Rightarrow 0 = m (\frac{l}{t} + v) + M v$
$v = - \frac{m l + t}{M + m} i . e \frac{m l / t}{M + m}$ towards left
$∴$ velocity of insect w.r.t ground $= \frac{l}{t} - \frac{m l / t}{M + m} < \frac{l}{t}$