Question

# If the gravitational potential due to the earth at infinite distance from it is zero, the potential at a point P is −5 J kg−1. Suppose we arbitrarily assume the gravitational potential at infinity to be +10 J kg−1. Then, gravitational potential at P will be

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

## The correct option is B +5 J kg−1Given that, Potential at P, VP=−5 J kg−1 The gravitational potential is a scalar quantity and change in gravitational potential doesn’t depend on the reference chosen. For 1st case: ΔV=VP−V∞ ⇒ΔV=−5 J/kg−1 For 2nd case: ΔV=VP−V∞ ⇒VP=V∞+ΔV ⇒VP=10−5 ⇒VP=+5 J kg−1 Hence, option (b) is correct. Why this question? To familiarize students with the concept of gravitational potential and that it doesn’t depend on the reference chosen.

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