Question

Assertion: Two bodies of masses M and m $\left( {M > m} \right)$ are allowed to fall from the same height if the air resistance for each be the same then both the bodies will reach the earth simultaneously.
Reason: For same air resistance, acceleration of both the bodies will be same.

A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.

Answer 1

Hint:First know about what are the conditions for the free fall of a body. Here two bodies of different masses fall from the same height and air resistance for both the bodies is also the same. We have to find whether the acceleration depends on the mass of the body or not.


Formula used
Acceleration, $a = \dfrac{{Force}}{{mass}}$
For free fall, $a = \dfrac{{g*mass - force}}{{mass}}$
$a = g - \dfrac{{force}}{{mass}}$$$


Complete answer:
Start with the given information:
Two bodies of mass M and m are given.
Also, M>m
Height is the same for both the bodies.
We know that;
Acceleration, $a = \dfrac{{Force}}{{mass}}$
Now, in case of free fall we know that;
Acceleration, $a = g - \dfrac{{force}}{{mass}}$
As the mass of the body is different, the acceleration for both the bodies will also be different.
As, M>m
So, ${a_1} \ne {a_2}$
Their acceleration is not the same for the same air resistance.
Therefore, both bodies will not reach the earth simultaneously.
It means both the Assertion and Reason is wrong.

Hence, the correct answer is Option D.


Note: Be aware of all the conditions in case of a free fall of a body of certain mass that is falling from a certain given height. Also know how to find the acceleration of the given body and whether the acceleration of the given body depends on the mass of the given body or not.