Question

ample 10.1 The mass of the earth is
6 X 1024 kg and that of the moon is
7.4 x 1022 kg. If the distance between
the earth and the moon is 3.84x105km,
calculate the force exerted by the earth
on the moon. G = 6.7 x 10-11 N m2 kg-2.
ution:​

Answer 1

Answer:

The Force exerted is 2*10²⁰ N.

Explanation:

Mass of Earth = 6*10²⁴ kg

Mass of Moon = 7.4*10²² kg

Distance between them = 3.84*10⁵ km or, 3.84*10⁸ m

G = 6.7*10⁻¹¹ N.m²/kg²

Force = [Gm₁m₂]/d²

= [{6.7*10⁻¹¹} * {6*10²⁴} * {7.4*10²²}] / (3.84*10⁸)²  N

= [{6.7*6*7.4} * {10⁻¹¹⁺²⁴⁺²²}] / 1.47*10¹⁷  N

= [297.48*10³⁵] / 1.47*10¹⁷    N

= 202.3*10¹⁸   N

= 2*10²⁰ N

Hope this helps.

Answer 2

Given -

• Mass of earth (M) = $\sf \ 6 \times {10}^{24} \: kg$

• Mass of Moon (m) = $\sf \ 7.4 \times {10}^{22} \: kg$

• Distance between them = $\sf \ = > 3.8 \times {10}^{5}km \: = 3.84 \times {10}^{8} \: m$

• G (universal gravitation constant) = $\sf\ 6.67 \times {10}^{ - 11} {n \: m}^{2} \: {kg}^{2}$

Formula used :-

$\sf \ F = \frac{G \times M \times m}{d ^{2} }$

Solution -

$\large\sf\frac{6.67 \times10^{ - 11}N \: m ^{2} {Kg}^{2} \times 6 \times {10}^{24}Kg \times 7.4 \times {10}^{22}Kg}{(3.84 \times {10}^{8})^{2} }$

$\sf\ = > 2.01 \times {10}^{20} \: N$