Question

g. The mass of the earth is 6x 10-4 kg.
The distance between the earth and
the Sun is 1.5x 1011 m. If the
gravitational force between the two
is 3.5 x 1022 N, what is the mass of
the Sun?
Use G= 6.7 x 10-11 N m2 kg?
Ans: 1.96 x 105 kg​

Answer 1

Given :

Gravitational force = GMm/r^2 =  1.5x 1011 m

Mass of earth = 6x 10-4 kg

Distance between the earth and the sun =  1.5x 1011 m

G = 6.7 x 10-11 N m2

g = GMm/r^2

3.5 x 1022  = (6.7 x 10^-11 × 6x 10^-4 × m) / (1.5x 10^11)

m = (3.5 x 10^22) × (1.5x 10^11) / (6.7 x 10^-11 × 6x 10^-4)

m = 1.96 × 10^5 kg

If you have any other queries you can write in the comments.

Answer 2

Correction in question :

Since mass of earth is known to all i.e. 6 × 10²⁴ kg

Answer:

1.96 × 10³⁰ kg

Explanation:

We have given :

m₁ =  6 × 10²⁴ kg

m₂ = we have to find it.

r = 1.5 × 10¹¹ m

F = 3.5 × 10²² N

G = 6.7 × 10⁻¹¹ N m² / kg²

We know :

F = G m₁ m₂ / r²

= > ( 3.5 × 10²² ) = ( 6.7 × 10⁻¹¹ ) . ( 6 × 10²⁴ ) ( m₂ ) / (  1.5 × 10¹¹ )²

= > ( 3.5 × 10²² ) = ( 6.7 ) . ( 6 × 10¹³ ) ( m₂ ) / (  1.5² × 10²² )

= >  ( 3.5 × 10²² ) = ( 6.7 ) . ( 6 ) ( m₂ ) / (  1.5² × 10⁹ )

= >  ( 3.5 × 10³¹ ) = ( 6.7 ) . ( 6 ) ( m₂ ) / (  1.5² )

= > m₂ = ( 3.5 × 10³¹ × 2.25 ) / ( 40.2 ) kg

= > m₂ = ( 78.75 × 10³⁰ ) / ( 40.2 ) kg

= > m₂ = 1.96 × 10³⁰ kg

Hence we get required answer!