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Physics-

General

Easy

Question

A vertical spring with force constant $K$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$ . The net work done in the process is

$m g + (h + d) + \frac{1}{2} K d^{2}$
$m g (h + d) - \frac{1}{2} K d^{2}$
$m g (h - d) - \frac{1}{2} K d^{2}$
$m g (h - d) + \frac{1}{2} K d^{2}$

The correct answer is: $m g open parentheses h plus d close parentheses minus fraction numerator 1 over denominator 2 end fraction K d to the power of 2 end exponent$

Gravitational potential energy of ball gets converted into elastic potential energy of the spring $m g open parentheses h plus d close parentheses equals fraction numerator 1 over denominator 2 end fraction K d to the power of 2 end exponent$
Net work done $equals m g open parentheses h plus d close parentheses minus fraction numerator 1 over denominator 2 end fraction K d to the power of 2 end exponent equals 0$

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