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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 end in time t, moving with a constant speed.


Correct Answer
A
The speed of the insect as seen from the ground is <lt
Correct Answer
B
The speed of the strip as seen from the ground is lt(mM+m)
Your Answer
C
The speed of the strip as seen from the ground is  lt(MM+m)
Your Answer
D
The total kinetic energy of the system is  12(m+M)(lt)2

Solution

The correct options are
A The speed of the insect as seen from the ground is <lt
B The speed of the strip as seen from the ground is lt(mM+m)

A Centre of mass of block

B Centre of mass of insect

Let 'C' Be centre of mass of system
where CA=x

mx=m(l2x)

(M+m)x=ml2

x=m(M+m)l2       (i)

Now, as the insect reaches the other end the displacement of centre of mass should be zero as there is no external force on the wood -insect system.

As evident from the diagram, the displacement of centre of mass of block is '2x'

From eq (i) 2x=mM+ml
Speed = 2xt=l2m(M+m)

Distance covered by insect from ground frame = (l-2x)

Speed of insect = l2xt, which is less than lt
 

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