question_answer

Two bodies of masses M and m (M > m) are allowed to fall from the same height. If the air resistance for each be the same, then will both the bodies reach the ground simultaneously?

Answer:

                The heavier body will reach the ground first as is explained below. Let F be the air resistance on each body. Then acceleration of the body of mass M is \[{{\text{a}}_{\text{1}}}=\frac{Mg-F}{M}=g-\frac{F}{M}\]The acceleration of the body of mass m is \[\frac{mg-F}{m}=g-\frac{F}{m}\] As, \[\text{M}>\text{m}\], so \[{{\text{a}}_{\text{1}}}>{{\text{a}}_{\text{2}}}\]. Therefore, the body of mass M (i.e. heavier body) will reach ground first.