Question

# The gravitational potential due to earth at infinite distance from it is zero. Let the gravitational potential at a point P be −5 Jkg−1. Suppose, we arbitrarily assume the gravitational potential at infinity to be +10 Jkg−1 , then the gravitational potential at P will be

A
5 J kg1
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B
+5 Jkg1
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C
15 Jkg1
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D
+15 Jkg1
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Solution

## The correct option is B +5 Jkg−1Case I: Gravitational Potential due to Earth at infinity, V∞=0, Gravitational Potential due to Earth at point P, VP=5 Jkg−1, So, the change in potential, ΔV=VP−V∞=−5−0=−5 Jkg−1 Simlarly, for Case II: Gravitational Potential due to Earth at infinity, V∞=10 Jkg−1, The change in gravitational potential doesn’t depend upon the reference points, so the change will remain same. So, the change in potential, ΔV=−5 ⇒VP−V∞=−5 ⇒VP−10=−5 ⇒VP=−5+10 ∴VP=+5 Jkg−1 Hence, option (b) is the correct answer. Alternative Solution: According to the problem as the potential at infinity increases by +10 J kg−1. The potential will increase by the same amount everywhere (since, potential gradient will remain constant). Hence, new potential point at point P=10−5=+5 J kg−1 Why this question: To familiarize students with the concept of gravitational potential and that it doesn’t depend upon the reference chosen.

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