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.
• B. $A$ will go higher than $B$.
• C. $B$ will go higher than $A$.
• D. any of the above three may happen depending on the speed with which the objects are thrown.
  

Answer 1

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 $F_R$ due to air will be exerted in the opposite direction we get,
$-F_R=m_A\times a_A$

$\Rightarrow a_A=\frac{-F_R}{m_A}$, for the object $A$,

$\Rightarrow a_B=\frac{-F_R}{m_B}$, for the object $B$
Where $a_A$ is the deceleration of body $A$ and $a_B$ is the deceleration of body $B$.

As it is given $m_A>m_B$, we get $|a_A|<|a_B|$
Hence $A$ will go higher than $B$.