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physics

mechanics

Easy

Question

A body weighs 250 N on the surface of the earth. How much will it weigh half way down to the centre of the earth?

175 N
125 N
150 N
250 N

The correct answer is: 125 N

Let m be mass of a body
$therefore$ Weight of the body on the surface of the earth is
$table attributes columnalign left end attributes row cell W equals m g equals 250 N end cell row cell g to the power of apostrophe equals g open parentheses 1 minus d over R subscript z close parentheses end cell row cell W equals m g to the power of apostrophe equals m g open parentheses 1 minus d over R subscript E close parentheses end cell row blank end table$
Here, $d equals R subscript E over 2$ $therefore W equals m g open parentheses 1 minus fraction numerator R subscript E divided by 2 over denominator R subscript E end fraction close parentheses equals fraction numerator m g over denominator 2 end fraction equals W over 2 equals fraction numerator 250 N over denominator 2 end fraction equals 125 N$

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