Question

If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct ?

• A. Raindrops will fall faster.
• B. Time period of a simple pendulum on the Earth would decrease.
• C. Walking on the ground would become more difficult.
• D. 'g' on the Earth will not change.

Answer 1

The Correct Option is D

To solve this problem, we need to understand the implications of two hypothetical changes: the mass of the Sun being ten times smaller and the universal gravitational constant being ten times larger. Let's analyze each option:

1. Raindrops will fall faster.
   • The force of gravity on raindrops is dependent on the gravitational acceleration g on Earth. If g increases, raindrops will indeed fall faster.
2. Time period of a simple pendulum on the Earth would decrease.
   • The time period T of a simple pendulum is given by T = 2\pi \sqrt{\frac{L}{g}}, where L is the length of the pendulum and g is the gravitational acceleration.
   • If g increases, the time period T decreases, making pendulums swing faster.
3. Walking on the ground would become more difficult.
   • If g increases, the force with which we are pulled towards Earth becomes stronger, thus increasing the difficulty of walking.
4. 'g' on the Earth will not change.
   • The acceleration due to gravity g on the surface of the Earth is calculated by g = \frac{GM}{R^2}, where G is the gravitational constant, M is the Earth's mass, and R is the Earth's radius.
   • If the gravitational constant G becomes ten times larger, g will increase significantly.
   • Thus, the statement "'g' on the Earth will not change" is incorrect.

Based on the step-by-step evaluation above, we can conclude that the hypothetical changes would indeed affect g on Earth, making the option "'g' on the Earth will not change" incorrect.