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If the mass of the sun were ten times sm...

 If the mass of the sun were ten times smaller and gravitational constant G were ten times larger in magnitude. Then,

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

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`implies` Given , `G. = 10 G`
Consider the adjacent diagram.
`=(G.M_em)/R^2=(10GM_em)/(R^2) " "[:. G. = 10G]`
`=10 ((GM_em)/R^2)`
`=(10 g)m=10 mg " "[ :. g = (GM_e)/R^2]" "...(1)`
Force on the object due to the sun `F = (GM._sm)/r^2`
`=(G(M_s)m)/(10r^2) " " [:. M._s =M_s/10` (given)]
For `r gt gt R` , F will be very small
So, the effect of the sun will be neglected.
Now, as g. = 10 g
Hence, weight of person = mg. = 10 mg 
[from Eq. (i)]
Hence, gravity pull on the person will increase. Due to it, walking on ground would become more difficult.
Critical velocity, v. is proportional to g i.e.,
`v_c prop g`
As, ` v_c gt v_c " " ( :. g. gt g)`
Hence, rain drops will fall much faster. To overcome the increased gravitational force of the earth, the aeroplanes will have to travel much faster.
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