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

#### Options

The two bodies will reach the same height.

A will go higher than B.

B will go higher than A.

Any of the above three may happen depending on the speed with which the objects are thrown.

#### Solution

A will go higher than B.

Let the air exert a constant resistance force = F (in downward direction).

Acceleration of particle A in downward direction due to air resistance, a_{A} = F/m_{A}.

Acceleration of particle B in downward direction due to air resistance, a_{B} = F/m_{B}.

m_{A} > m_{B}

a_{A} < a_{B}

\[S = ut + \frac{1}{2}a t^2\]

\[So, H_A = ut - \frac{1}{2}( a_A + g) t^2\]

\[H_B = ut - \frac{1}{2}( a_B + g) t^2\]

\[H_A > H_B\]

Therefore, A will go higher than B.