Question

Assertion: A particle follows only a parabolic path if acceleration is constant.
Reason: The projectile motion path is parabolic, as acceleration is assumed to be constant at low heights.

A. If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
B. If both Assertion and Reason are true and the Reason is not the correct explanation of the Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false, but the Reason is true.

Answer 1

First we need to study the assertion and reason properly. Then we are considering a case to check that the assertion is true or false. We need to check that the assertion satisfies all the cases or not. Then we need to check the reason. For checking the reason we need to know the formula for trajectory of a projectile motion.

Formula used:
$y=x\tan \theta -\dfrac{g{{x}^{2}}{{\sec }^{2}}\theta }{2{{V}_{0}}^{2}}$

Complete step by step answer:
Here the assertion is given as, a particle follows only a parabolic path if acceleration is constant.
And the reason is stated as, the projectile motion path is parabolic, as acceleration is assumed to be constant at low heights.
So to see that the assertion is true or false we are considering a case

In the above diagram a particle is travelling in ‘x’ direction and its velocity is ‘u’. The particle is also accelerating in the same direction that is ‘x’.
So considering this case we can see that the particle will always follow a straight line motion. And its acceleration is also constant. So we can say that the assertion statement is false.
Now we are considering the reason given in the question,
We know that, in projectile motion equation of trajectory is,
$y=x\tan \theta -\dfrac{g{{x}^{2}}{{\sec }^{2}}\theta }{2{{V}_{0}}^{2}}$ ,
In the above equation, we consider ‘g’ as a constant, so it is an equation of the parabola , and in projectile motion, parabolic path is always followed, so since acceleration due to gravity is assumed constant in y-direction hence the path followed by the body of object is parabolic and we can get the path from the equation of motion. So the reason statement is true.
So, we can say that option D, that is If Assertion is false, but the Reason is true, is the correct answer.

Note:
In the equation $y=x\tan \theta -\dfrac{g{{x}^{2}}{{\sec }^{2}}\theta }{2{{V}_{0}}^{2}}$, if ‘g’ would not be stated as constant then it would not have been an equation of projectile and the reason would be false. We are checking the assertion to verify that the assertion is always correct in every case.