If the mass of sun were len times smaller and gravitational consitant `G` were ten times larger in magnitudes

Options

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

A, C, D

Explanation

New mass of Sun, `M._(s) = M_(s)//10`
New gravitational constant, G. = 10 G
New gravitational force between the earth and the sun will be
`F_(S.) = (G.M_(s)M_(E))/(R^(2)) = ((10 G)(M_(S)//10)M_(E))/(R^(2))`
`= (GM_(S)M_(E))/(R^(2)) = F_(S)`
So, the gravitational force between the earth and the sun remains same.
But as the value of G has increased, the gravitational force exerted by the earth on the nearby region increases.
Acceleration due to gravity will also become 10 time as `g prop G`. So, weight of a person mg will also increases. This implies that walking on ground will become more difficult.
Due to increased value of g, raindrops will be accelerated more and hence, their velocity will increase.
In order to overcome the increased gravitational pull of earth, airplanes will have to travel faster.
The correct options are (a), (c ) and (d).