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.

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)
C
The speed of the strip as seen from the ground is  lt(MM+m)
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(l2−x) ⇒(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 = l−2xt, which is less than lt

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