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Gravitational Potential Energy

The total mec...

Question

The total mechanical energy E possessed by a body of mass 'm', moving with a velocity 'v' at a height 'h' is given by : $E = \frac{1}{2} m v^{2} + m g h .$ Make 'm' the subject of formula.

m = \frac{2 E}{v^{2} + g h}

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m = \frac{2 E}{v^{2} + 2 g h}

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m = \frac{3 E}{v^{2} + 2 g h}

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m = \frac{E}{v^{2} + 2 g h}

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Solution

The correct option is B $m = \frac{2 E}{v^{2} + 2 g h}$
$E = \frac{1}{2} m v^{2} + m g h$
Multiply both side 2:
$2 E = m v^{2} + 2 m g h$
Or $2 E = m (v^{2} + 2 g h)$
Or $m = \frac{2 E}{v^{2} + 2 g h}$

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