Find the acceleration due to gravity in a mine of depth 640m if the value at the surface is 9.800 ms-². The radius of the earth is 6400 km.

Asked by yogendramishra0404 | 4th Nov, 2015, 07:46: AM

Expert Answer:

The value of acceleration due to gravity at depth 'd' below the surface of the Earth is 
begin mathsize 12px style straight g apostrophe space equals space straight g space open parentheses 1 space minus space straight d over straight R close parentheses where space straight g space equals space 9.8 space straight m divided by straight s squared comma space space straight d space equals space 640 space straight m space and space straight R space equals space 6.4 space cross times space 10 to the power of 6 straight m Substituting space the space values space in space the space equation comma space we space get straight g apostrophe space equals space 9.8 space open parentheses 1 space minus space fraction numerator 640 over denominator space 6.4 space cross times space 10 to the power of 6 end fraction close parentheses straight g apostrophe space equals space 9.799 space straight m divided by straight s space squared end style

Answered by Yashvanti Jain | 4th Nov, 2015, 11:39: AM