Question

A body P has mass 2 m and velocity 5v. Another body Q of mass 8 m and velocity 1.25 v. Find out the ratio of momentum of P and Q
A. 2:1
B. 1:1
C. 1:2
D. 3:2

Answer 1

The momentum is the product of the mass of the body and the velocity of the body and using the definition of the momentum find the value of the momentum of the body P and the body Q. After finding the two momenta find the ratio of both quantities.

Complete step by step solution:
The momentum of any body can be defined as the product of the mass of the body and the velocity with which the body is moving.
We know the value of the mass of the body P is given as 2m
Where m is some unknown value
We know the given velocity of the moving body P is given as 5v
So the value of the momentum of the moving body P is obtained as :
P = mass $\times$ velocity
So the momentum is $M_P= 2m \times 5v$
We know the value of the mass of the body Q is given as 8m
Where m is some unknown value
We know the given velocity of the moving body P is given as 1.25v
So the value of the momentum of the moving body P is obtained as :
P = mass $\times$ velocity
$M_Q = 8m \times 1.25 v$
Now we have found the value of the momentum of both bodies and hence we can find the ratio of the momentum as :
Ratio = $\dfrac{M_P}{M_Q} = \dfrac{2m \times 5v}{8m \times 1.25 v} = 1 : 1$

Thus using the definition of the momentum we found the value of the ratio of the momentum as 1:1

Note: The quantity momentum is different from the quantity impulse and often these quantities are misunderstood. We need to understand that momentum is the product of the mass times velocity and the impulse of the change in the value of the momentum.