Question

Two spheres of the same size, one of mass $2kg$ and another of mass $4kg$ are dropped simultaneously from the top of Qutub Minar $\left(height=72m\right)$. When they are $1m$ above the ground, the two spheres have the same:

• A. Momentum
• B. Kinetic Energy
• C. Potential Energy
• D. Acceleration

Answer 1

The correct option is D

Acceleration

Correct Answer : Option (D)- Acceleration

1. Acceleration of a body is the rate of change of its velocity.
2. It is expressed as, $a=\frac{∆v}{∆t}$
3. It is independent of mass. Here, the velocity of the bodies will be same due to the gravitational acceleration.
4. Hence, the acceleration of the bodies will be the same at the same heights.

Incorrect Answers:

1. Option A: Momentum: It can be defined as the product of mass and velocity. It is expressed as, $p=mv$. It depends on mass. Since the mass of the bodies are different, they won't possess the same momentum at the same height.
2. Option B: Kinetic Energy: It can be defined as the energy possessed by a body due to its motion. It is the product of half of mass and square of velocity. It depends on mass. It is expressed as, $KE=\frac{1}{2}m{v}^2$. Since the mass of the bodies are different, they won't possess the same kinetic energy at the same height.
3. Option C: Potential Energy: It can be defined as the energy possessed by a body due to its height. It is the product of mass, acceleration due to gravity, and height. It depends on mass. It is expressed as, $PE=mgh$. Since the mass of the bodies are different, they won't possess the same potential energy at same height.

Hence, the correct option is option d.