Question

The momentum p of an object varies with time (t) as shown in figure. The corresponding force (F) - time (t) graph is 

A. 

B. 

C. 

D. 

Answer 1

Hint: In the question, the momentum time graph is given. We have to find the force time graph using this. The force is given as the derivative of momentum with respect to time. In a graph, derivative of the momentum is given as the slope of momentum time graph. These all may help us to solve this question.

Complete step-by-step answer:
First of all let us discuss the momentum of a particle in detail. Momentum is defined as the product of the mass of a particle and its velocity. Isaac Newton's second law of motion tells that the time rate of change of momentum is proportional to the force experienced on a body. The momentum of a rigid body is basically the sum of the momenta of Individual particle in the body. For this question we can see that the momentum time graph has been provided in the question from which we have to derive the force time graph.
As we all know,
Force is given as the rate of change of momentum. Therefore taking the derivative of the value of momentum can give us the force. For that we can use the technique of taking the slope of the momentum time graph which is equivalent to the time derivative of the momentum.
Therefore we can write that,
$F=\dfrac{dP}{dt}$
For the interval $0 < t < 2$,
$\dfrac{dP}{dt}=5$
For the interval $2 < t < 6$,
$\dfrac{dP}{dt}=0$
For the interval $6 < t < 8$,
$\dfrac{dP}{dt}=-5$
Plotting this on the graph paper will give the graph similar to option A. Therefore the correct answer is obtained.

So, the correct answer is “Option A”.

Note: There are two kinds of momentum generally. They are linear and angular momentum. A spinning object is having angular momentum. An object traveling with a velocity is pursuing linear momentum. Momentum is a vector quantity which is having direction useful for the prediction of the resulting direction and speed of motion of particles after a collision.