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JEE Main 2015 (11 Apr, Shift 1) · Gravitational Potential & Energy

Gravitational Potential & Energy question from JEE Main 2015 (11 Apr, Shift 1)

Q26JEE Main 2015 · 11 APR · SHIFT 1Medium

Gravitational Potential & Energy

Which of the following most closely depicts the correct variation of the gravitation potential V(r) due to a large planet of radius R and uniform mass density? (figuresarenotdrawntoscale)

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Answer: (b)

Inside: $V = -\frac{GM(3R^2 - r^2)}{2R^3}$ , a parabola with minimum $-\frac{3GM}{2R}$ and zero slope at the centre.
Outside: $V = -\frac{GM}{r}$ , negative and rising towards zero.
Potential is negative everywhere, smooth at $R$ , flat-bottomed at $r = 0$ .
So the answer is (b).

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