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JEE Main 201910 AprilMorning Shift

Exam: JEE Main
Year: 2019
Date: 10 April
Shift: Morning Shift
Subject: Physics
Chapter: Gravitation

JEE Main 2019 · 10 April · Morning Shift · Physics · Gravitation

The value of acceleration due to gravity at Earth's surface is 9.8m...

The value of acceleration due to gravity at Earth's surface is

9.8m{s}^{- 2}

. The altitude above its surface at which the acceleration due to gravity decreases to

4.9m{s}^{- 2}

, is close to: (Radius of earth

= 6.4 \times {10}^{6}m

)

Options

A $1.6 \times {10}^{6}m$
B $2.6 \times {10}^{6}m$
C $6.4 \times {10}^{6}m$
D $9.0 \times {10}^{6}m$

Correct answer

B. $2.6 \times {10}^{6}m$

Step-by-step solution

Acceleration due to gravity

g = \dfrac{GM}{{R}^{2}}

.......(1)

⇒ \dfrac{g}{2} = \dfrac{GM}{{( R + h )}^{2}}

............(2)
From (1) and (2),

\dfrac{GM}{2{R}^{2}} = \dfrac{GM}{{( R + h )}^{2}}

R + h = \sqrt{2}R

h = 0.414 \times 6.4 \times {10}^{6}

= 2.6 \times {10}^{6}\text{m}

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