Question

A body P has a mass of 2 m and velocity of 5 v. Another body Q has a mass of 8 m and velocity of 1.25 v. The ratio of momentum of P and Q is :

• A. 2:1
• B. 1:1
• C. 1:2
• D. 3:2

Answer 1

The correct option is B

1:1

Given:

masses (m) and velocities (v) of body P and Q

$$\begin{gathered} m_P=2m \\ {v}_P=5v \\ {m}_Q=8m \\ {v}_Q=1.25v \end{gathered}$$:

Calculating Momentum for body P and Q

As we know, the Momentum of the body is the product of mass and velocity.

$p=mv$

Where, p = momentum of the body

m = mass of the object

v = velocity of the object

so, momentum of P, $p_P=m_P{v}_P=2m\times 5v=10mv$

and momentum of Q, $p_Q=m_Q{v}_Q=8m\times 1.25v=10mv$

The calculating ratio of momentum of P & Q

$\frac{p_P}{p_Q}=\frac{10mv}{10mv}=1:1$

So the ratio of their momentum is 1:1.

Hence option (b) is correct.