Question

Which of the following is true of changes in momentum?

A small force may produce a large change in momentum by acting over a short time interval.

A large force may produce a small change in momentum by acting over a short time interval.

A small force may produce a large change in momentum by acting on a very massive object.

A small force may produce a large change in momentum by acting over a short distance.

can you please explain why this is the answer as well and how you got it?

Answer 1

Answer: ⇒  Answer is 3

Explanation: momentum = mass × velocity

"A small force may produce a large change in momentum by acting on a very massive object".

THEY HAVEN'T GIVEN US THE TIME PERIOD NOR THE DISTANCE TRAVELED. THEREFORE WE CANNOT ACTUALLY DECIDE IF THE FORCE IS KEPT FOR A LONG TIME OR SHORT TIME. ANYWAYS SINCE THE MASS IS GIVEN AS MASSIVE , THE  MOMENTUM SHOULD BE DEFINITELY HIGH.

WHY I SAY OTHERS ARE WRONG:

1) For a small force to give a large change in momentum, it should act for a long time interval.

2) By applying a large force for a short time interval, the change of momentum should be large.

3) Correct answer.

4) Acting over a short distance can be the same as acting over a short period of time.Therefore the distance should be large in order for a larger momentum.

I HOPE IT HELPS!

Answer 2

The true statement is required.

The true statement is A large force the change in momentum may be small acting over a short time interval.

Force is given by

$F=ma$

m = Mass of object

a = Acceleration = $\dfrac{v-u}{t}$

t = Time

So, force is

$F=m\dfrac{v-u}{t}\\\Rightarrow F=\dfrac{mv-mu}{t}\\\Rightarrow F=\dfrac{\Delta p}{t}$

$\Delta p$ = Change in momentum.

If the time taken is small then the force will be large.

The change in momentum can also be small.

So, for a large force the change in momentum may be small acting over a short time interval.

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