Question

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following {Assume negligible air friction}

• A. Time taken by them to reach the earth's surface will be independent of the properties of their materials.
• B. Insulating ball will reach the earth's surface earlier than the metal ball.
• C. Both will reach the earth's surface simultaneously.
• D. Metal ball will reach the earth's surface earlier than the insulating ball.

Hint:

Without air friction both balls fall with the same acceleration \(g\), so the fall time \(\sqrt{2h/g}\) is identical for both.

Answer 1

The Correct Option is C

Step 1: Free fall.
When air friction is ignored, each ball is acted on by weight only. We write $mg = ma$, so $a = g$ for every ball, whatever it is made of.

Step 2: Use the equation of motion.
Starting from rest, the distance fallen is $h = \frac{1}{2}gt^2$. Solving for time gives
\[ t = \sqrt{\frac{2h}{g}} \]

Step 3: Apply it to the two balls.
Here $h$ is the same for both and $g$ is the same at that place. So $t$ is the same number for both balls.
A ball being a conductor or an insulator changes nothing in this formula.

Step 4: Rule out the unequal-time options.
Options (B) and (D) each name a winner. Our result gives no winner, so neither can be right. Only the statement that the two land together matches the calculation.

Final Answer:
The two balls land together. The answer is option (C). \[ \boxed{\text{C}} \]