Gravitational potential energy associated with two point masses, each of 1 kg, separated by a distance of 1cm in Joule is (G= gravitational constant)
- 2G
- 100G
- 1000G
- G
- 500G
The Correct Option is B
Approach Solution - 1
The formula for gravitational potential energy \(U\) between two point masses \(m_1\) and \(m_2\) separated by a distance \(r\) is given by: \[ U = -\frac{G m_1 m_2}{r} \] Where:
\(G\) is the gravitational constant,
\(m_1 = m_2 = 1 \, \text{kg}\),
\(r = 1 \, \text{cm} = 0.01 \, \text{m}\).
Substituting the values: \[ U = -\frac{G \cdot 1 \cdot 1}{0.01} = -\frac{G}{0.01} = -100G \] Since the gravitational potential energy is negative (by convention), the magnitude is \(100G\).
The correct option is (B) : \(100\ G\)
Approach Solution -2
The gravitational potential energy between two point masses is given by:
$$ U = -\frac{G m_1 m_2}{r} $$
Here, \( m_1 = 1\, \text{kg} \), \( m_2 = 1\, \text{kg} \), \( r = 1\, \text{cm} = 0.01\, \text{m} \)
Substituting the values: $$ U = -\frac{G \cdot 1 \cdot 1}{0.01} = -\frac{G}{0.01} = -100G $$
The magnitude of gravitational potential energy is 100G J.
Correct answer: 100G
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