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Question

A running man has the same kinetic energy as that of a boy of half his mass. The man speeds up by 2 m/s and the boy changes his speed by x m/s so that the kinetic energies of the boy and the man are again equal. Then x in m/s is

A
32
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B
22
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C
2
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D
2
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Solution

The correct option is B 22
Let m be mass of the man, vm be speed of the man and
m/2 be mass of the boy, vb be speed of the man
Initially, KE of man = KE of boy
12mv2m=12(m2)v2bvb=2vm
In the second case,
12m(vm+2)2=12(m2)(vb+x)2
vm+2=12[vb+x]=12[2vm+x]
vm+2=vm+x2
x2=2x=22
Hence, the correct answer in option (b).

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