Question

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 of the strip and walks to the other in time l sec moving with constant speed is then

• A. Speed of insect as seen from ground is $<\frac{1}{1}$
• B. speed of insect as seen from ground is = $\frac{u}{1}$($\frac{M}{M+m}$)
• C. speed of insect as seen from ground is = $\frac{2u}{1}$($\frac{M}{M+m}$)
• D. speed of insect as seen from ground is = $\frac{u}{1}$($\frac{3M}{M+m}$)

Answer 1

The correct option is B speed of insect as seen from ground is = $\frac{u}{1}$($\frac{M}{M+m}$)

After the insect sits on wood, all forces/ motion now occur internally

to the wood insect system.

As external force = 0. the COM of wood insect will remain at rest.

Now, insect covers length = 1 m in time t = 15.

so speed of insect, u = 1/1 = 1 m/s.

using conservation of momentum

mu = v(m+n) [$v=$ velocity of wood wrt ground]

$\Rightarrow V=\frac{mu}{(M+m)}$ (Reqd)