Question

A body X of mass 5 kg is moving with velocity 20 m/s while another body Y of mass 20 kg is moving with velocity 5 m/s. Compare the momentum of the two bodies.

Answer 1

Use the formula that momentum of a particle is nothing but the product of their velocity and mass, Now calculate the momentum of both the bodies and divide them to compare.

Complete step-by-step answer :
Given:
Body X:
Mass, 5 kg
Velocity, 20 m/s

Body Y:
Mass, 20 kg
Velocity, 5 m/s

Calculation:
The momentum of the object is given as:
P = mv

Where, m is the mass of the object and v is the speed of the object

For Body X:
The momentum is given as:
${P}_{1}=mv$
${P}_{1}$ = (5 kg) (20 m/s)

For Body Y:
The momentum is given as:
${P}_{1}=mv$
${P}_{2}$ = (20 kg) (5 m/s)

The ratio of momentum is given as:
$\begin{aligned} & \Rightarrow \dfrac{{{P}_{1}}}{{{P}_{2}}}=\dfrac{5\times 20}{20\times 5} \\\ & \Rightarrow {{P}_{1}}:{{P}_{2}}=1:1 \end{aligned}$

Note :The comparison of the momentum can also be calculated using the difference of the momentum of the two quantities.
The difference in the momentum is given as:
$\begin{aligned} & \Rightarrow \Delta P={{P}_{1}}-{{P}_{2}} \\\ & \Rightarrow \Delta P=\left( 20\times 5 \right)-\left( 5\times 20 \right) \\\ & \Rightarrow \Delta P=0 \\\ \end{aligned}$
As the difference in the momentum of the two quantities is zero. The momentum of both objects is equal.