A) \[4.2\times {{10}^{6}}\,m\]
B) \[3.19\times {{10}^{6}}\,m\]
C) \[1.59\times {{10}^{6}}\,m\]
D) None of these
Correct Answer: A
Solution :
Radius of earth R = 6400 km \ \[h=\frac{R}{4}\] Acceleration due to gravity at a height h \[{{g}_{h}}=g{{\left( \frac{R}{R+h} \right)}^{2}}\]\[=g{{\left( \frac{R}{R+\frac{R}{4}} \right)}^{2}}\]\[=\frac{16}{25}g\] At depth 'd' value of acceleration due to gravity \[{{g}_{d}}=\frac{1}{2}{{g}_{h}}\] (According to problem) Þ \[{{g}_{d}}=\frac{1}{2}\left( \frac{16}{25} \right)g\]\[\Rightarrow g\left( 1-\frac{d}{R} \right)\]\[=\frac{1}{2}\left( \frac{16}{25} \right)\ g\] By solving we get\[d=4.3\times {{10}^{6}}m\]
You need to login to perform this action.
You will be redirected in
3 sec
