Question

Let the mass of sun be ten times smaller and gravitational constant $G$ be ten times larger in magnitudes. Then, find the incorrect statement among the given ones.

• A. Walking on ground would become more difficult.
• B. The acceleration due to gravity on earth will not change.
• C. Raindrops will fall much faster.
• D. Airplanes will have to travel much faster.

Answer 1

Answer: (B)

When $G$ increases ten times, the acceleration due to gravity on earth becomes
$g'=\frac{\left(10 G\right) \left(M_{E}\right)}{R_{E}^{2}}=\frac{10 G M_{E}}{R_{E}^{2}}=10g \, \left(\right.\because g=\frac{G M_{E}}{R_{E}^{2}}\left.\right)$
Hence, statement (B) is incorrect.
$\therefore $ Weight of person = $mg^{'}=m\left(10 g\right)=\left(\right.10mg\left.\right)$
where $m$ is the mass of the person
Gravity pull on person will increase. Due to it, walking on ground would become more difficult.
Hence, (C) is a correct statement.
To overcome the increase gravitational pull of earth, the aeroplanes will have to travel much faster.
Terminal speed of rain drop, $ \, v_{T}=\frac{2 \, r^{2}}{9}\frac{\left(\right. \rho - \sigma \left.\right) g}{\eta}$
where the symbols have their usual meanings.
Since $v_{T} \propto $ $g$ , as $g$ increases, $v_{T}$ increases.
Hence, (C) is a correct statement.
To overcome the increase gravitational pull of earth, the aero planes will have to travel much faster.