Question

An iron sphere of mass $10kg$ has the same diameter as an aluminum sphere of mass $3.5kg.$ Both spheres are dropped simultaneously from a tower. When they are $10m$above the ground, they have the same:

• A. Acceleration
• B. momentum
• C. Potential energy
• D. Kinetic energy

Answer 1

The correct option is A

Acceleration

Explanation for the correct answer:

In free fall, acceleration due to gravity of both the bodies does not dependent of mass. Hence, both the bodies will have the same acceleration.

Explanation for Incorrect answer:

1. Potential energy of a body is directly proportional to the mass of the body.

$$\begin{gathered} P.E.=mgh \\ P.E.\propto m \end{gathered}$$

2. Kinetic energy of a body is directly proportional to the mass of the body.

$$\begin{gathered} K.E.=\frac{1}{2}m{v}^2 \\ K.E.\propto m \end{gathered}$$

3. Momentum of a body also depends upon the mass of the body.

$p=mv$

Thus, when the given bodies are $10m$ above the ground, they have the same value of acceleration.

Hence, option A is correct.