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 the earth will not change
C. raindrops will fall much faster
D. airplanes will have to travel much faster

Answer

A, C, D

Explanation

Given, `G' = 10 G`
Consider the adjacent diagram.

Force on the object due to the earth `= (G'M_(e)m)/(R^(2)) = (10 GM_(e) m)/(R^(2))" " [:. G' = 10 " given "]`
`= 10 ((GM_(e)M)/(R^(2)))`
`= (10 g) m = 10 mg [:. g = (GM_(e))/(R^(2))]`.....(i)
Force on the object due to the sun `F = (GM'_(s)m)/(r^(2))`
`= (G(M_(s))m)/(10 r^(2)) [:. M'_(s) = (M_(s))/(10) ("given")]`
As `r gt gt R` (radius of the earth) `rArr F` will be very small.
So, the effect of the sun will be neglected
Now, as `g' = 10 g` [from Eq. (i)]
i.e., gravity pull on the person will increase. Due to it, walking on ground would become more difficult.
Critical velocity, `v_(c)` is proportional to g i.e.,
`v_(c) prop g`
As `g' gt g`
`rArr v_(c) gt v_(c)`
Hence, rain drops will fall much faster.
To overcome the increased gravitational force earth, the aeroplans will have to travel much faster