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
$g^{\prime }=\frac{\left(10G\right)\left(M_E\right)}{R_E^2}=\frac{10G{M}_E}{R_E^2}=10g(\because g=\frac{G{M}_E}{R_E^2})$
Hence, statement (B) is incorrect.
$\therefore$ Weight of person = $m{g}^{{}^{\prime }}=m\left(10g\right)=(10mg)$
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, $v_T=\frac{2r^2}{9}\frac{(\rho -\sigma )g}{\eta }$
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.