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Question

Two objects A and B are thrown upward simultaneously with the same speed. The mass of A is greater than the mass of B. Suppose the air exerts a constant and equal force of resistance on the two bodies then,

A
the two bodies will reach the same height.
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B
A will go higher than B.
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C
B will go higher than A.
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D
any of the above three may happen depending on the speed with which the objects are thrown.
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Solution

The correct option is B A will go higher than B.
We know that force due to air resistance provides deceleration, if deceleration of the body is high, body travels less distance.

As the force of resistance FR due to air will be exerted in the opposite direction we get,
FR=mA×aA

aA=FRmA, for the object A,

aB=FRmB, for the object B
Where aA is the deceleration of body A and aB is the deceleration of body B.

As it is given mA>mB, we get |aA|<|aB|
Hence A will go higher than B.

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