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Question

Figure shows two small blocks placed on a smooth horizontal surface. They start moving from the same line with force 2F and F respectively acting on the blocks. Their momenta and kinetic energies at the instants of crossing the finishing line as shown in figure are pA,pB and KA,KB. Then choose the correct option.


A
KA=KB,pA=pB
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B
KA>KB,pA>pB
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C
KA>KB,pA<pB
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D
KA>KB,pA=pB
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Solution

The correct option is D KA>KB,pA=pB
Let the displacement of the two blocks on the smooth horizontal surface be 'S'.

Work done in moving block A, (WA)=2FS

Work done in moving block B, (WB)=FS

From work-energy theorem,
Work done = change in kinetic energy
Since the blocks are initially at rest, we can write that,
WAWB=KAKB

KAKB=2FSFS=21...(1)

Hence, KA>KB

But, kinetic energy (K)=p22m
KA=p2A2mA and KB=p2B2mB
From this ,
KAKB=p2Ap2B×mBmA
Using (1) and the data given in the question

21=p2Ap2B×2mmpA=pB

Thus, option (d) is the correct answer.

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