Question

A heavy truck and bike are moving with same kinetic energy. If the mass of the truck is four times that of the bike, then calculate the ratio of momenta.

Answer 1

Let the mass of the Nike be m. Thus mass of the truck will be 4m.

Let the velocity of the Bike be v and the velocity of the truck be V.

Since, they are having the same kinetic energy.

Thus, 1/2 mv² = 1/2 MV²

mv² = 4mV²

v² = (2V)²

v = 2V

For the Ratio of the Momentum,

Momentum of bike/Momentum of car = mv/MV

= m(2V)/(4m)V

= 2/4

= 1/2

Ratio of Momentum of truck to bike = 2/1.

Hope it helps.