An object is dropped from rest at a height of $150\, m$ and simultaneously another object is dropped from rest at a height $100 \,m$. What is the difference in their heights after $2\,\sec $ if both the objects drop with same accelerations ? How does the difference in heights vary with time ?

Initial difference in height $=(150-100) \,m =50 \,m$

Distance travelled by first body in $2 \,s=h_{1}=0+\frac{1}{2}\, g(2)^{2}=2\, g$

Distance travelled by another body in $2 \,s=h_{2}=0+\frac{1}{2} \,g(2)^{2}=2 \,g$

After $2 \,s$, height at which the first body will be $= h _{1}^{\prime}=150-2\, g$

After $2\, s,$ height at which the second body will be $= h _{2}^{\prime}=100-2\, g$

Thus, after $2\, s$, difference in height $=150-2\, g -(100-2\, g )$

$=50 \,m =$ initial difference in height

Thus, difference in height does not vary with time.