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: Understanding the Concept:
With negligible air friction, the only force on each ball is gravity. A falling body then moves under free fall, and free fall does not depend on what the body is made of.

Step 2: Key Formula or Approach:
Newton's second law gives \(ma = mg\), so the acceleration is \(a = g\). The mass cancels. For a drop from rest through height \(h\):
\[ h = \tfrac{1}{2} g t^2 \quad \Rightarrow \quad t = \sqrt{\frac{2h}{g}} \]

Step 3: Detailed Explanation:
Both balls have the same size and the same mass, and both are dropped from the same height \(h\) with zero initial speed.
The time \(t = \sqrt{2h/g}\) contains only \(h\) and \(g\). It has no term for the material, conductivity or charge of the ball.
So the metallic ball and the insulating ball take exactly the same time to reach the ground.
Option (B) says the insulating ball lands first and option (D) says the metal ball lands first. Both are wrong, because the equation gives one common time for the two balls.

Final Answer:
Both balls reach the ground at the same instant, so the correct option is (C). \[ \boxed{\text{(C) Both will reach the earth's surface simultaneously.}} \]