Two objects A and B are projected upward at the same time with...

Let the initial speed of both objects be $u$.

The retardation of an object of mass $m$ moving upwards under gravity and a constant air resistance $F$ is given by $a = g + \dfrac{F}{m}$.

For object $A$, $a_A = g + \dfrac{F}{m_A}$.

For object $B$, $a_B = g + \dfrac{F}{m_B}$.

Since $m_A > m_B$, we have $\dfrac{F}{m_A} < \dfrac{F}{m_B}$, which implies $a_A < a_B$.

The maximum height reached by the object is $H = \dfrac{u^2}{2a}$.

Since $a_A < a_B$, we get $H_A > H_B$.

Thus, object $A$ reaches a greater height than object $B$.