Question

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.

Answer 1

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.