Question

Q32. A body weighs 25kg on the surface of the Earth, if the mass of the earth is 6x1024 kg ,the radius of
the earth is 6.4x10m and the gravitational constant 6.7x10-'Nm?kg-2.​

Answer 1

Answer:

Q32. A body weighs 25kg on the surface of the Earth, if the mass of the earth is 6x1024 kg ,the radius of

the earth is 6.4x10m and the gravitational constant 6.7x10-'Nm?kg-2.

Explanation:

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Answer 2

Correct Question :

A body weighs 25kg on the surface of the Earth, If the mass of the earth is 6 × 10²⁴ kg , the radius of

the earth is 6.4 x10⁶ m and the gravitational constant 6.67 × 10⁻¹¹ Nm².Kg⁻². Then find the graviational force of attraction between the body and earth

Given :

• mass of the body = 25kg
• Mass of the earth = 6 × 10²⁴ kg
• Radius of the earth = 6.4 × 10⁶ m
• Gravitational constant = 6.67 × 10⁻¹¹ N.m².Kg²

To find :

• The fore of gravitation between the body and earth

Solution :

The relation between masses , gravitational constant , radius and force of attraction is ,

$\boxed {\rm{F= \frac{Gm_1m_2}{r {}^{2} } }}$

We have ,

• G = 6.67 × 10⁻¹¹ N.m².kg⁻²
• r = 6.4 × 10⁶ m
• m₁ = 25 kg
• m₂ = 6 × 10²⁴ kg

By substituting the values ,

$: \implies \rm \: F = \frac{(6.67 \times 10 {}^{ - 11} \: N.m {}^{2}. {kg}^{ - 2} )(25 \: kg)(6 \times {10}^{ 24} \: kg) }{(6.4 \times {10}^{ 6} \: m) {}^{2} } \\ \\ : \implies \rm \: F = \frac{(6.67 \times {10}^{ - 11} \: N.m {}^{2}.kg {}^{ - 2} )(150 \times {10}^{ 24} \: kg {}^{2}) }{40.96 \times 10 {}^{12} \: m {}^{2} } \\ \\ : \implies \rm \: F= \frac{(6.67 \times {10}^{ - 11} \: N. \cancel{m {}^{2}.kg {}^{ - 2}}) (150 \times {10}^{ 24} \cancel{ kg {}^{2}} ) }{40.96 \times {10}^{ 12 } \cancel{m {}^{2} }} \\ \\ : \implies \rm \: F = \frac{(6.67 \times {10}^{ - 11} \: N)(150 \times {10}^{ 24} )}{40.96 \times {10}^{12} } \\ \\ : \implies \rm \: F = \frac{1000.5 \times {10}^{13} \: N}{40.96 \times {10}^{12} } \\ \\ : \implies \rm \: F= \frac{1000.5 \times 10 \: N }{40.96} \\ \\ : \implies \rm \: F = 244.2 \: N$

∴ The Force of attraction between the body and earth is 244.2 N