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Question

Physics Question on Gravitation

The value of acceleration due to gravity at a depth of 1600 km1600\, km is equal to (Given Radius of earth=6400km)

A

9.8 ms−29.8 \, ms^{-2}

B

4.9 ms−24.9 \, ms^{-2}

C

19.6 ms−219.6 \, ms^{-2}

D

7.35 ms−27.35\, ms^{-2}

Answer

7.35 ms−27.35\, ms^{-2}

Explanation

Solution

Given.
Depth (d)=1600 km(d)=1600 \,km
We know that,
gd=g(1−dR)g_{d} =g\left(1-\frac{d}{R}\right)
Here g=9.8 m/s2g=9.8 \,m / s ^{2}
R=6400 kmR=6400 \,km
gd=g(1−16006400)g_{d} =g\left(1-\frac{1600}{6400}\right)
=9.8(1−14)=9.8\left(1-\frac{1}{4}\right)
=9.8(4−14)=9.8×34=9.8\left(\frac{4-1}{4}\right)=\frac{9.8 \times 3}{4}
gd=7.35 ms−2g_{d} =7.35 \,ms ^{-2}