A running man has the same kinetic energy as that of a boy of half his mass. The man speed up by 2 m s- 1 and the boy changes his speed by x m s- 1 , so that the kinetic energies of the boy and the man are again equal. Then x in m s- 1 is

Question

A running man has the same kinetic energy as that of a boy of half his mass. The man speed up by 2 m s- 1 and the boy changes his speed by x m s- 1 , so that the kinetic energies of the boy and the man are again equal. Then x in m s- 1 is (A) 4√2 (B) 2√2 (C) √2 (D) 2

Tardigrade Admin · Accepted Answer

Let vM be velocity of man and vB of boy, then kinetic energy according to question , i.e.K=(1/2)MvM2=(1/2).(M/2).vB2 Or vM2=(VB2/2) Or √ 2vM=vB When the man speeds up 2ms- 1 and the boy changes his speed by x ms- 1 .Then , (1/2)M(vM + 2)2=(1/2)⋅ (M/2)⋅ (vB + x)2 Or (vM + 2)2=((vB + x)2/2) 2(vM + 2)2=(√2 vM + x)2 (∵ vB = √2 vm) Or √2(vM + 2)=√2vM+x Or x=2√2

Q. A running man has the same kinetic energy as that of a boy of half his mass. The man speed up by $2 m s^{- 1}$ and the boy changes his speed by $x m s^{- 1}$ , so that the kinetic energies of the boy and the man are again equal. Then $x$ in $m s^{- 1}$ is

$42$

$22$

$2$

$2$

Q. A running man has the same kinetic energy as that of a boy of half his mass. The man speed up by 2ms−1 and the boy changes his speed by xms−1 , so that the kinetic energies of the boy and the man are again equal. Then x in ms−1 is

42​

22​

2​

2

Q. A running man has the same kinetic energy as that of a boy of half his mass. The man speed up by $2 m s^{- 1}$ and the boy changes his speed by $x m s^{- 1}$ , so that the kinetic energies of the boy and the man are again equal. Then $x$ in $m s^{- 1}$ is

$42$

$22$

$2$

$2$