Question

If the mass of sun were ten times smaller and gravitational constant G were ten times larger in magnitudes ______.

1. walking on ground would became more difficult.
2. the acceleration due to gravity on earth will not change.
3. raindrops will fall much faster.
4. airplanes will have to travel much faster.

Answer 1

a, c and d

Explanation:

Given, G' = 10 G

Consider the adjacent diagram

Force on the object due to the earth = `(G'M_em)/R^2 = (10Gm_em)/R^2`  ......[∵ G' = 10 g given]

= `10 ((GM_em)/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^3`

= `(G(M_s)m)/(10r^2)`  ......`[∵ M_s = M_s/10 ("given")]`

As r >> R (radius of the earth) = F will be very small.

So, the effect of the sun will be neglected.

Now, as g' = 10g

Hence, weight of person = mg’ = 10 mg .....[From equation (i)

i.e., gravity pull on the person will increase. Due to it. walking on the ground would become more difficult.

Critical velocity, v, is proportional to g i.e., 

v_c ∝ g

As g' > g

⇒ v_c > v_c

Hence, raindrops will fall much faster.

To overcome the increased gravitational force of the earth, aeroplanes will have to travel much faster.