JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Gravitation

The approximate height from the surface of earth at which the weight of the body becomes

\frac{1}{3}

of its weight on the surface of earth is : [Radius of earth

R = 6400 km

and

3 = 1.732

]

(A)3840 km
(B)4685 km✓ Correct
(C)2133 km
(D)4267 km

Answer: (B)

Solution

The acceleration due to gravity at height

h

g^{'} = g (\frac{R}{R + h})^{2}

.

For weight to become

\frac{1}{3}

g^{'} = \frac{g}{3}

(\frac{R}{R + h})^{2} = \frac{1}{3}

\frac{R}{R + h} = \frac{1}{3}

R + h = R 3

h = R (3 - 1) = 6400 (1.732 - 1) = 6400 \times 0.732 = 4684.8 \approx 4685 km

JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Single correct option

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