Question

The masses of two bodies are 100 kg and 50 kg respectively. If the gravitational force of attracation between them is 5×10-8N,calculate the distance between the objects.
G=6.7×10-11Nm2/kg2

Answer 1

Answer:-

Given:

Mass of 1st body (M) = 100 kg

Mass of 2nd body (m) = 50 kg

Gravitational force between them (F) = 5 × $\sf {10}^{ - 8}$ N

G (Gravitional Constant) = 6.7 × $\sf {10}^{-11}$ Nm²/kg².

Let the Distance between them be r.

We know that,

F = GMm/r²

Hence,

$\sf \implies \: 5 \times {10}^{ - 8} = \dfrac{6.7 \times {10}^{ - 11} \times 100 \times 50}{ {r}^{2} }$

$\sf \implies \: {r}^{2} \times 5 \times {10}^{ - 8} = 6.7 \times {10}^{ - 11} \times 1 \times 5 \times {10}^{3}$

$\sf \implies \: {r}^{2} = \dfrac{6.7 \times {10}^{ - 11} \times {10}^{3} \times 5 }{5 \times {10}^{ - 8} }$

Using the Formulae a^m × a^n = a^(m + n) and a^m/a^n = a^(m - n) we get,

$\sf \implies \: {r}^{2} = 6.7 \times {10}^{[( - 11 + 3) - ( - 8)]}$

$\sf \implies \: {r}^{2} = 6.7 \times {10}^{0}$

Using a⁰ = 1 we get,

→ r² = 6.7

→ r = √6.7

→ r = 2.5 m

Therefore, the distance between the bodies is 2.5 m.

Answer 2

Explanation:

According to Newton's Law of Gravitation:

F = Gm1m2/r²

Given; m1 is 100 kg, m2 is 50 kg, F is 5 × 10^-8N and G is 6.7 × 10^-11 Nm²/kg².

Substitute the values to find the value of r i.e. distance between them.

→ 5 × 10^-8 = (6.7 × 10^-11 × 100 × 50)r²

→ r² = (6.7 × 5000 × 10^-11)/(5 × 10^-8)

→ r² = (33500 × 10^(-11 + 8))/5

→ r² = 6700 × 10^-3

→ r = √6.7

→ r = 2.6

Hence, the distance between the two bodies of mass 100 kg and 50 kg is 2.6 m.