JEE Main 2015 · 11 Apr · Shift 1 · Physics Q7

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PhysicsSingle correct+4 / -1Question 7 of 90

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 ? (figures are not drawn to scale)

V rises linearly to a peak and then falls

Graph of V(r) against r, with O at the origin: a straight rise from O to a peak, then a decreasing curve.

V negative, rising smoothly from a minimum at the centre towards zero

Graph of V(r) against r, with O at the origin: negative throughout: a flat-bottomed minimum near O, rising smoothly towards zero.

V constant (negative) inside, then rising towards zero outside

Graph of V(r) against r, with O at the origin: a constant negative value up to some r, then a curve rising towards zero.

V positive, falling from a maximum at the centre towards zero

Graph of V(r) against r, with O at the origin: positive, flat near O and falling to a small value at large r.

Answer and worked solution

Official answer: B

Inside, $V=-\dfrac{GM(3R^2-r^2)}{2R^3}$ , a downward parabola with its minimum $-\frac32\frac{GM}R$ at the centre. Outside, $V=-\dfrac{GM}r$ , rising towards zero. So V is negative everywhere and rises smoothly from the centre: graph (2).

Topics:Gravitational field and potential

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JEE Main 2015 · 11 Apr · Shift 1, Physics question 7