A feather weighing 5 g and a nail weighing 10 g have the same kinetic energy. Which of the following statements is true about the momentum of the two bodies?

Options

A. The heavier body will have higher momentum
B. Both will have equal momentum
C. It is not possible to compare the momentum of two objects
D. The lighter body will have higher momentum

Answer

A

Explanation

Momentum, `P=sqrt(2mk)`
For mass of 5 g, momentum
`P_(1)=sqrt(2kxx5)=ksqrt(10)`
For mass of 10 g, momentum
`P_(1)=sqrt(2kxx5)=ksqrt(10)`
For mass of 10 g, momentum
`P_(2)=sqrt(2kxx10)=ksqrt(20)`
implies `Palphasqrt(m)` (if k = constant)
`therefore (P_(1))/(P_(2))=sqrt((m_(1))/(m_(2)))`
Therefore, the heavier body will have higher momentum.