Question

Two objects of masses 5 kg and 10 kg are placed 2 meters apart. What is the gravitational force between them?
(Use \(G = 6.67 \times 10^{-11}\, \mathrm{Nm^2/kg^2}\))

• A. \(1.67 \times 10^{-10}\) N
• B. \(8.34 \times 10^{-11}\) N
• C. \(3.34 \times 10^{-10}\) N
• D. \(5.00 \times 10^{-N}\)

Hint:

Use Newton's law of gravitation: \(F = G \frac{m_1 m_2}{r^2}\), carefully square the distance.

Answer 1

The Correct Option is A

- Given:
Mass \( m_1 = 5\, \mathrm{kg} \), Mass \( m_2 = 10\, \mathrm{kg} \), Distance \( r = 2\, \mathrm{m} \), Gravitational constant \( G = 6.67 \times 10^{-11}\, \mathrm{Nm^2/kg^2} \)

- Gravitational force is given by Newton’s law of gravitation:
\[ F = G \frac{m_1 m_2}{r^2} \]

- Substitute values:
\[ F = 6.67 \times 10^{-11} \times \frac{5 \times 10}{(2)^2} = 6.67 \times 10^{-11} \times \frac{50}{4} = 6.67 \times 10^{-11} \times 12.5 = 8.3375 \times 10^{-10}\, \mathrm{N} \]

- Rounded to \(1.67 \times 10^{-10}\) N (check options carefully):
Actually, the above result is \(8.34 \times 10^{-10}\) N, which matches none exactly, but the closest option is (A) \(1.67 \times 10^{-10}\) N if there is a typo in options.

- Rechecking calculation carefully:
\[ F = 6.67 \times 10^{-11} \times \frac{5 \times 10}{4} = 6.67 \times 10^{-11} \times 12.5 = 8.3375 \times 10^{-10} \]

So the force is approximately \(8.34 \times 10^{-10}\) N, closest to none of the given options exactly. Maybe the options have a typo or intended to be \(10^{-10}\) scale. If the distance is 5 m instead of 2, force reduces.

Assuming options typo, the answer is:

\[ \boxed{8.34 \times 10^{-10} \, \mathrm{N}} \]

If we consider options as is, option (B) \(8.34 \times 10^{-11}\) N is 10 times less than the calculation. So please verify question data.

Answer: \(\boxed{\text{None exactly, but closest is (B) } 8.34 \times 10^{-11} \text{ N}}\)