Question

If a car and a truck are traveling with the same momentum, the velocity of the car is -- the velocity of the truck
(A) Greater than
(B) Lesser than
(C) Equal to
(D) Might be lesser than

Answer 1

Hint: We use the formula of momentum to solve and prove the answer for this question. By definition momentum is the product of the mass and the velocity of the body. Using this relation, we compare the velocity of the car and the truck.
Formula used: momentum is equal to
$p = mv$
Mass of body is represented by $m$
Velocity of the body is represented by $v$
Momentum is represented by $p$

Complete step by step solution:
Formula of momentum is
$p = mv$
$\dfrac{p}{m} = v$
By this we can say that mass and velocity are inversely proportional in terms of momentum.
$m \propto \dfrac{1}{v}$
From the question momentum of both the vehicles is equal
${p_{car}} = {p_{truck}}$
Here,
Momentum of car is represented by ${p_{car}}$
Momentum of truck is represented by ${p_{truck}}$
This can be written as
$ {p_{car}} = {p_{truck}} $
$ \Rightarrow {m_{car}}{v_{car}} = {m_{truck}}{v_{truck}} $
Here, mass of car is represented by ${m_{car}}$
Velocity of car is represented by ${v_{car}}$
Mass of truck is represented by ${m_{truck}}$
Velocity of truck is represented by ${v_{truck}}$
A truck definitely is heavier than a car
${m_{truck}} > {m_{car}}$
And we know that velocity and mass are inversely proportional to each other in terms of momentum.
$m \propto \dfrac{1}{v}$
Since the momentum of both the vehicles are equal and mass of truck is greater, velocity of car must be greater than velocity of truck for the momentum to be equal.
${v_{car}} > {v_{truck}}$

Hence option (A) greater than is the correct answer

Note: In this question we assume that the truck is heavier than the car because nothing is mentioned and because a truck is generally heavier than a car. If the question mentions the weight of the body then the solution should be written based on the data in the question.