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Question

A running man has half the kinetic energy that a boy of half his mass has.The man speeds up by 1ms1 and then has the same kinetic energy as that of the boy. The original speeds of man and boy in ms1 are:

A
(2+1),(21)
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B
(2+1),2(2+1)
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C
2,2
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D
(2+1),2(21)
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Solution

The correct option is B (2+1),2(2+1)
Let,
m be the mass of the man,
m be the mass of the boy,
v be the velocity of the man,
v be the velocity of the boy.

As per the question,

12mv2=12(12mv2)
12mv2=14mv2
12mv2=14m2v2
v=v2
v=2v

In later case

12m(v+1)2=12mv2
12m(v+1)2=12(m2)(2v)2
12m(v+1)2=mv2
v2+2v+1=2v2
v22v1
v22v=1
v22v+1=2
(v1)2=2
v1=2
v=2+1
and v=2v
v=2(2+1)

Therefore, the speed of man is 2+1 and the speed of boy is 2(2+1).

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