Question

A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by 1 m/s so as to have the same K.E. as that of the boy. The original speed of the man will be:

विकल्प

• `sqrt2  "m"//"s"`

• `(sqrt2 - 1)"m"//"s"`

• `1/((sqrt2 - 1)) "m"//"s"`

• `1/sqrt2 "m"//"s"`

Answer 1

`1/((sqrt2 - 1)) "m"//"s"`

Explanation:

Let m = mass of boy, M = mass of man

v = velocity of boy, V = velocity of man

`1/2 "MV"^2 = 1/2[1/2 "mv"^2]` ....(i)

`1/2 "M" ("V" + 1)^2 = 1[1/2 "mv"^2]` ...(ii)

Putting m = `"M"/2` and solving V = `1/(sqrt2 - 1)`