Question

If the mass of sun were ten times smaller and gravitational constant G were ten times larger in magnitudes, then which one of the following statement is incorrect?

• 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 safer.

Answer 1

The correct option is D Airplanes will have to travel much safer.

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 = ${mg}^{\prime }=m\left(10g\right)=10mg$
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, (a) is a correct statement.
Terminal speed of rain drop, $v_T=\frac{2}{9}\frac{r^2(\rho -\sigma )g}{\eta }$
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 increasing gravitational pull of the earth, the aeroplanes will have to travel much faster.