Question

Two objects X and Y are thrown upwards simultaneously with the same speed. The mass of X is greater than that of Y. The air exerts equal resistive force on two objects, then

• A. X will be higher than Y
• B. Y will higher than X
• C. The two objects will reach the same height
• D. cannot say

Answer 1

The correct option is A X will be higher than Y

Let the mass of the object A be $m_x$ and of object B be $m_y$ where $m_x>m_y$. Let the resistive force applied by air on the objects be F. Let the height reached by object X be $H_x$ and by object Y be $H_y$ . Let the speed they are launched be v. The balls will reach maximum height when their Kinetic Energy becomes zero. Writing the required equation we have;
$\frac{1}{2}\times m_x\times v^2-F\times H_x-m_{x}g{H}_x=0$
$\frac{1}{2}\times m_y\times v^2-F\times H_y-m_{y}g{H}_y=0$
Simplifying above we have;
$H_x=\frac{\frac{1}{2}\times m_x\times v^2}{F+m_{x}g}$
$H_y=\frac{\frac{1}{2}\times m_y\times v^2}{F+m_{y}g}$
Dividing above two we have;
$\frac{H_x}{H_y}=\frac{m_x\times (F+m_{y}g)}{m_y\times (F+m_{x}g)}$
$\frac{H_x}{H_y}=\frac{m_{x}F+m_x{m}_{y}g}{m_{y}F+m_y{m}_{x}g}$
Since $m_x>m_y$ we have $H_x>H_y$.