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 analyze the effects of changing the mass of the Sun and the gravitational constant on various phenomena. Let's break down each option by considering the physics involved:

1. Effect on Raindrops: The terminal velocity of raindrops is influenced by gravitational force. The gravitational force has the mass of Earth, not the Sun, as its sole influential factor by \( F = \frac{G M m}{r^2} \). Here, changing the mass of the Sun or the gravitational constant does not affect the Earth’s local gravitational field. But increasing the gravitational constant might affect the speed of raindrops, causing them to fall faster.
2. Effect on Pendulum: The period of a simple pendulum is given by \( T = 2\pi \sqrt{\frac{l}{g}} \). Since 'g' determines the time period, and 'g' is the gravitational acceleration of Earth given by \( g = \frac{G M_e}{R_e^2} \) (where \( G \) is universal gravitational constant, \( M_e \) the mass of Earth, and \( R_e \) the radius of Earth), increasing \( G \) would indeed increase 'g' and thus decrease the time period of the pendulum.
3. Effect on Walking: Walking is based on frictional and gravitational forces. If the gravitational acceleration increases due to a higher gravitational constant, walking would require more energy as the effective weight would increase, making walking more difficult.
4. Value of 'g' on the Earth: The acceleration due to gravity 'g' is dependent on \( G \) and \( M_e \) as indicated earlier. With \( G \) increasing by ten times, 'g' will also increase linearly. Hence, the statement "'g' on the Earth will not change" is incorrect in this scenario.

Conclusion: Considering the explanations provided, the correct answer is that it is not true that "'g' on the Earth will not change." If the universal gravitational constant increases, then 'g' would indeed increase, making this statement false.