JEE Main 2017 · 9 Apr · Shift 1 · Physics Q7

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PhysicsSingle correct+4 / -1Question 7 of 90

The mass density of a spherical body is given by $\rho(r)=\dfrac kr$ for r ≤ R and ρ(r) = 0 for r > R, where r is the distance from the centre.

The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is :

Rising linearly to a peak at R, then falling

a against r: rising linearly from zero to a peak at R, then falling off as 1/r².

Constant up to R, then falling

a against r: constant from r = 0 to R, then falling off as 1/r².

Rising ever more steeply to a peak at R, then falling

a against r: rising from zero, curving upward, to a peak at R, then falling off.

Falling slowly up to R, then falling faster

a against r: starting high at r = 0 and decreasing slowly to R, then falling off faster.

Answer and worked solution

Official answer: B

Inside, $M(r)=\int_0^r4\pi r'^2\frac k{r'}dr'=2\pi kr^2$ , so $a=\dfrac{GM(r)}{r^2}=2\pi Gk$ , a constant. Outside, $a\propto\frac1{r^2}$ . That is graph (2).

Topics:Gravitational field and potential

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JEE Main 2017 · 9 Apr · Shift 1, Physics question 7