Question

Two objects $A$ and $B$ are thrown upwards 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 $B$

There are only two forces acting on both the masses. These are the gravitational force and air resistance. Both of these forces are equal in magnitude for both the masses.

Let the effect of these forces be R.

Thus, we get $m_A{a}_A=R$,

and $m_B{a}_B=R$

where deceleration of A$=\left(a_A\right)$ and deceleration of B $=\left(a_B\right)$.

As the mass of A is greater than B, so the deceleration$\left(a_A\right)$ of A is less than of deceleration $\left(a_B\right)$of B.

We know that, Height is given as:

$H=\sqrt{\frac{u^2}{2a}}$.

As the initial velocity ($u$) is same for A and B, so $H_A$ is greater than $H_B$.

Therefore, A will go higher than B.