Question

An iron sphere of mass $30\mathrm{kg}$ has the same diameter as an aluminum sphere mass is $10.5\mathrm{kg}$. The spheres are dropped simultaneously from a cliff. When they are $10\mathrm{m}$ from the ground, they have the same

• A. acceleration
• B. momentum
• C. potential energy
• D. K.E.

Answer 1

The correct option is A

acceleration

The explanation for the correct option:

The correct option is A. acceleration

1. For any free-falling body, the acceleration of the body is equal to the acceleration due to gravity.
2. The acceleration due to gravity is independent of the mass of the body.
3. For the two spheres, having a mass of $30\mathrm{kg}$ (iron) and $10.5\mathrm{kg}$ (aluminum) respectively, their acceleration is the same when they are dropped simultaneously from a cliff.
4. Hence, an iron sphere and the aluminum sphere will have the same acceleration when they are $10\mathrm{m}$ from the ground.

The explanation for the incorrect options:

B. momentum

The momentum of a body depends on its mass. Since the mass of the two spheres is different, their momentum will differ.

$P=MVwhewmismass,Visvelocity$

C. potential energy

The potential energy of a body depends on its mass. Since the mass of the two spheres is different, their potential energy will differ.

$$\begin{gathered} PE=Mgh \\ mismass,hisheight \end{gathered}$$

D. K.E.

The kinetic energy (K.E.) of a body depends on its mass. Since the mass of the two spheres is different, their potential energy K.E. will differ.

$KE=\frac{1}{2}M{V}^2$

Hence, the correct option is A.