Question

A motorcycle and a truck are both moving in the same direction in adjacent lanes on a highway. At a particular instant, the speed of motorcycle is four times as large as the speed of truck v. At that instant, motorcycle is accelerating forward while the truck is moving at a constant velocity. Which one of the following statements best describes which vehicle has a larger momentum at that instant?
A. The truck, because it has a larger mass
B. The motorcycle, because it is moving faster
C. The motorcycle, because it has an acceleration
D. The motorcycle, because it is moving faster and also has an acceleration
E. Not enough information to answer

Answer 1

As a very first step, one could read the question properly and hence note down the given conditions. There are two instants given and you could search for some way to do a comparison of the momentums of these bodies. Recall the expression for linear momentum for better understanding.

Complete step-by-step solution:
We see that in the question we are given a truck and a motorcycle and we are supposed to compare their momentum. We are two instants. One where the speed of the motorcycle is four times that of truck (v). That is,
${{v}_{m}}=4v$……………………………………………… (1)
Another instant where the motorcycle is accelerated forward while the truck maintains constant velocity. We are well aware of the fact that acceleration has nothing to do with finding the momentum at a particular instant.
For the previous instant,
Momentum P could be given by,
P=mv
From (1), if the mass of the truck has been more than 4 times more massive than the motorcycle, we could have concluded that the momentum of the truck is greater.
But no information on the mass of the two bodies is given other than logic than the truck would be way more massive than a motorcycle. So mathematical comparison is impossible here.
Hence, option E. Not enough information to answer is correct.

Note: If the mass of the truck has been less than four times the mass of the motorcycle, we could have concluded that the momentum of the motorcycle is more. Also, if the mass of the truck has been equal to 4 times the mass of the bike, we could say that their momentums are equal.