First slide

Conservation of mechanical energy

Question

A machine which is 75 percent efficient, uses 12 joules of energy in lifting up a 1 kg mass through a certain distance. The mass is then allowed to fall through that distance. The velocity at the end of its fall is (in ${ms}^{- 1})$

Moderate

A

$\sqrt{24}$
B

$\sqrt{32}$
C

$\sqrt{18}$
D

$\sqrt{9}$

Solution

Potential energy of a body = 75% of 12 J
mgh = 9 J $\Rightarrow h = \frac{9}{1 \times 10} = 0 .9 m$
Now when this mass allow to fall then it acquire velocity
$v = \sqrt{2 gh} = \sqrt{2 \times 10 \times 0 .9} = \sqrt{18}$ m/s.

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