JEE Main · 2023 · 30 Jan 2023 · Shift 1 · Gravitation

If the gravitational field in the space is given as

(- \frac{K}{r ^{2}})

. Taking the reference point to be at

r = 2

cm with gravitational potential

V = 10

J/kg. Find the gravitational potential at

r = 3

cm in SI unit (Given, that

K = 6

J cm/kg)

(A)9
(B)11✓ Correct
(C)12
(D)10

Answer: (B)

Solution

Field and potential are linked by

g = - \frac{d V}{d r}

, and with

g = - \frac{K}{r ^{2}}

this gives

d V = \frac{K}{r ^{2}} d r

. Integrating from the reference point,

V (3) - V (2) = K [- \frac{1}{r}]_{2}^{3} = K (\frac{1}{2} - \frac{1}{3}) = \frac{K}{6}

. With

K = 6 J cm/kg

and

r

in centimetres this change is

1 J/kg

, so

V (3) = 10 + 1 = 11 J/kg

JEE Main · 2023 · 30 Jan 2023 · Shift 1 · Single correct option

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