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What is the Decrease in Weight of a Body of Mass 600kg When It is Taken in a Mine of Depth 5000m? - Physics

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Numerical

What is the decrease in weight of a body of mass 600kg when it is taken in a mine of depth 5000m?

[ Radius of earth = 6400km, g = 9.8 m/s2 ]

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Solution

Given that m = 600 kg, d = 5000 m,
R = 6400 km = 6.4 × 106m
Weight of the body on the surface of the Earth = 600 × 9.8 = 5880 N
At depth d, gravitation acceleration is

`g_d=g[1-d/R]`

`thereforeg_d=g[1-5/6400]=9.8 x 0.999`

`therefore g_d=9.7902`m/s2

Weight on surface = mg

                              =600 x 9.8

∴Weight on surface= 5880N

weight of the body at depth=mgd

                                            =600 x 9.7902

                                           =5874N

∴Decrease in weight = mg -mgd

                                  =5880 N - 5874 N

∴Decrease in weight = 6N

 
Concept: Acceleration Due to Gravity and Its Variation with Altitude and Depth
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