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Question

Physics Question on Gravitation

At what depth below the surface of the earth, acceleration due to gravity gg will be half its value 1600 km1600\,km above the surface of the earth?

A

4.2×106m4.2 \times 10^{6} m

B

3.19×106m3.19 \times 10^{6} m

C

1.59×106m1.59 \times 10^{6} m

D

none of these

Answer

4.2×106m4.2 \times 10^{6} m

Explanation

Solution

Variation of g outside the earth g1=g(1−2hR) g1=10(1−2×16006400) g1=5m/s2\begin{array}{l} g ^{1}= g \left(1-\frac{2 h }{ R }\right) \\\ g ^{1}=10\left(1-\frac{2 \times 1600}{6400}\right) \\\ g ^{1}=5 m / s ^{2} \end{array} Variation of g inside the earth g11=g(1−hR)g ^{11}= g \left(1-\frac{ h }{ R }\right) Now, it is given that, g11=g12 2.5m/s2=10(1−h6400) 14=1−h6400 h=34×6400Km h=4.8×106m\begin{array}{l} g^{11}=\frac{g^{1}}{2} \\\ 2.5 m / s ^{2}=10\left(1-\frac{ h }{6400}\right) \\\ \frac{1}{4}=1-\frac{ h }{6400} \\\ h =\frac{3}{4} \times 6400 Km \\\ h =4.8 \times 10^{6} m \end{array}