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A person trying to lose weight by burning fat lifts a mass of 10kg up to a height of 1m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies $3.8 \times {10^7}{\text{ }}J$ of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take $g{\text{ }} = {\text{ }}9.8{\text{ }}m{s^{ - 2}}$.(A) ${\text{6}}{\text{.45 x 1}}{{\text{0}}^{ - 3}}kg$(B) ${\text{9}}{\text{.89 x 1}}{{\text{0}}^{ - 3}}kg$(C) ${\text{12}}{\text{.89 x 1}}{{\text{0}}^{ - 3}}kg$(D) ${\text{2}}{\text{.45 x 1}}{{\text{0}}^{ - 3}}kg$

Last updated date: 04th Aug 2024
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Hint:Here efficiency is given 20% which means:
$Efficiency{\text{ }}\left( n \right){\text{ }} = {\text{ }}output/input.$ (Where output is work done)
Therefore, the fat used when weight is lifted by considering the input will be related with work done and fat supplied i.e,
$\Rightarrow Fat{\text{ }}used{\text{ }} = {\text{ }}Input/fat{\text{ }}supplied$
$\Rightarrow {{20}{l}}{ = {\text{ }}5 \times {{10}^5}{\text{ }}J/3.8 \times {{10}^7}{\text{ }}J} \\ \Rightarrow { = {\text{ }}12.89 \times {{10}^{ - 3}}{\text{ }}kg.}$

Here, we know that
$\Rightarrow {{20}{l}}{m{\text{ }} = {\text{ }}10kg,} \\ \Rightarrow {h{\text{ }} = {\text{ }}1m,} \\ \Rightarrow {n{\text{ }} = {\text{ }}1000}$
Work done in lifting mass = $n \times mgh$
$= 1000 \times 10 \times 9.8 \times 1 - - (1)$
If $m$ is mass of fat burnt, then energy gained
$= m \times 3.8 \times {10^7} \times \dfrac{{20}}{{100}} - - (2)$
If there is no loss of energy, then from (1) and (2)
$\Rightarrow m \times 3.8 \times {10^7} \times \dfrac{{20}}{{100}} = 1000 \times 10 \times 9.8 \\ \therefore m = \dfrac{{9.8 \times {{10}^4} \times 5}}{{3.8 \times {{10}^7}}} = 12.89 \times {10^{ - 3}}kg \\$
From the above calculations, we can conclude that $12.89 \times {10^{ - 3}}kg$ is the correct answer.

Hence,option (C) is the right answer.
Note:Here in the given question, the work done is considered when the weight is lifted and not when he lowers the mass because, while lifting the weight energy is consumed due to which the work is done against the gravitational force.