Question

Two stones of mass $m_1$ and $m_2$ (such that $m_1$ and $m_2$ ) are dropped $△$ t time apart from the same height towards the ground. At a later time t the difference in their speed is $△$ V and their mutual separation is $△$ S . While both stones are in flight

• A. $△$ V decreases with time and $△$ S increases with time.
• B. $△$ V and $△$ S increases with time.
• C. $△$ V remains constant time and $△$ S decreases with time.
• D. $△$ V remains constant time and $△$ S increases with time.

Answer 1

The correct option is D $△$ V remains constant time and $△$ S increases with time.

$\Delta V=g\Delta t$
Since $\Delta t$ is unchanged, $\Delta V$ remains same.
After some time t,
$\Delta S=\frac{g{t}^2}{2}-\frac{g(t-\Delta t{)}^2}{2}=\frac{1}{2}(2gt\Delta t+(\Delta t{)}^2)$
$\Delta S\propto t$ so $\Delta S$ increases with time.