Question

Two bodies of masses 10 kg and 100 kg are separated by a distance of 2m ( G = 6.67 × 10⁻¹¹ Nm² kg⁻²). The gravitational potential at the mid point on the line joining the two is(a) 7.3 × 10⁻⁷ J/kg(b) 7.3 × 10⁻⁹ J/kg(c) –7.3 × 10⁻⁹ J/kg(d) 7.3 × 10⁻⁶ J/kg

Answer 1

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Answer 2

Given :

Two bodies of masses 10 kg and 100 kg are separated by a distance of 2 m.

G = 6.67 × 10⁻¹¹ N m² kg⁻² .

To Find :

The gravitational potential at the mid point on the line joining the two bodies .

Solution :

We know , potential at a distance r is given by :

$P=-\dfrac{Gm}{r}$

So , potential due the mid-point is given by :

$P=P_1+P_2\\\\P=-\dfrac{Gm_1}{1}-\dfrac{Gm_2}{1}\\\\P=-G(m_1+m_2)\\\\P=-6.67\times 10^{-11}\times ( 10+100)\ J/kg\\\\P=-733.7\times 10^{-11}\ J/kg\\\\P=-7.3\times 10^{-9}\ J/kg$

Therefore , gravitational potential at the mid point on the line joining the two is -7.3 × 10⁻⁹ J/kg .

Learn More :

Gravitation

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