Ncert Exercises & Solutions

If the mass of the sun were ten times smaller and gravitational constant

$G$ were ten times larger in magnitude. Then,

(a)	walking on the ground would become more difficult.
(b)	the acceleration due to gravity on the earth will not change.
(c)	raindrops will fall much faster.
(d)	aeroplanes will have to travel much faster.

Choose the correct alternatives:
1. (a), (b), (c)
2. (a), (d)
3. (b), (c), (d)
4. (a), (c), (d)

Hint: Use Newton's law of gravitation.

Step 1: Find the force on an object on the surface of the Earth.

Given, ‘G’=10G
Consider the adjacent diagram.

Force on the object due to the earth

$= \frac{G' M_{e} m}{R^{2}} = \frac{10 G M_{e} m}{R^{2}} [∵ G' = 10 G$ ]

$= 10 (\frac{G M_{e} m}{R^{2}})$

$= (10 g) m = 10 m g [∵ g = \frac{G M_{e}}{R^{2}}] . . . (i)$

Force on the object due to the sun,

$F = \frac{G M'_{s} m}{r^{2}}$

$= \frac{G (M_{s}) m}{10 r^{2}} [∵ M'_{s} = \frac{M_{s}}{10} (g i v e n)]$

As r>> R(radius of the earth)

$\Rightarrow$ F will be very small.

So, the effect of the sun will be neglected.

Now, as g' =10 g

Hence, weight of person = mg' = 10mg [from Eq.(I)] i.e. gravity pull on the person will increase. Due to it, walking on the ground would become more difficult.

Step 2: Find the terminal velocity of the raindrops.
Critical velocity is proportional to g' i.e.

$v_{c} \propto g$ .

As g'>g

$\Rightarrow v_{c}' > v_{c}$

Hence, raindrops will fall much faster.

Step 3: Find the effect of the gravitational pull on the aeroplanes.
To overcome the increased gravitational force of the earth, the aeroplanes will have to travel much faster.

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