The kinetic energy of a man is half the kinetic energy of a body of half of his mass. If the man increases his speed by 1m/s then his kinetic energy becomes equal to that of the boy. The ratio of the velocity of the boy and that of the man is:
34
12
43
21
A
21
B
12
C
34
D
43
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Solution
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Let,
K and K′ be the kinetic energies of man and a boy respectively. Similarly, m and m′, v and v′ be the masses and velocities of man and a boy respectively.
Given that
K=12K′
m=2m′
v=v+1=v′′(say) ⇒K=K′
12mv2=1212m′v′2
⇒v2v′2=m′2m
∴v2v′2=m′4m′
∴vv′=12
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