Question

A sphere is projected horizontally with a speed $v$ from the edge of a table of height $h$ above a level horizontal floor. At the same instant, another sphere is released from the edge of the same table.
If the mass of the sphere that is released is doubled, and the mass of the projected sphere remains the same,identify which of the following statements is true?

• A. The two spheres will strike the floor at the same time
• B. The sphere that is dropped will strike the floor first
• C. The sphere that is launched horizontally will strike the floor first
• D. The acceleration of the sphere that is dropped is greater than the acceleration of the outer sphere after it is launched
• E. The acceleration of the sphere after it is launched is greater than the acceleration of the sphere that is dropped

Answer 1

Answer: (A)

The two spheres will strike the floor at the same time

Since the only force acting on the both the sphere is the gravitational force of attraction from earth only, the acceleration of both the sphere is $g$ downwards independent of the mass of the spheres.

Also the velocity of both the sphere initially in the vertical direction is zero,

$h=\frac{1}{2}g{t}^2$

$⟹t=\sqrt{\frac{2h}{g}}$ which is same for both the spheres.