Question

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

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

Answer 1

The correct option is C $g$ on earth will not change

Where a body thrown up from surface of earth, the acceleration due to gravity is outcome of gravitational pull due to earth.

$g=\frac{F_{grav}}{m}$

Since, $F_{grav}=\frac{G{m}_1{m}_2}{r^2}$

($m_1=$ mass of earth, $m_2=$ mass of body)

$\Rightarrow F_{grav}\propto G$

Increasing $G$ will increase $F_{grav}$, hence the value of acceleration due to gravity increases.

Change of value of $g$ will impact the velocity of rain drops.

Similarly, $f=\mu N=\mu mg$ (limiting value) will get affected, and it will influence the walking on ground.

Time period of pendulum is given as

$T=2\pi \sqrt{\frac{L}{g}}$

Hence, $T$ will also change.

Therefore, option $\left(c\right)$ is correct.

$$\begin{array}{c}\text{Why this question ?}\\ \text{Caution: As per law of gravitation,}\\ \text{the force experienced by a body in}\\ \text{gravitational field of earth will be}\\ \text{impacted by mass of earth and that}\\ \text{body. Hence mass of sun is given just to create confusion.}\end{array}$$