Tag: energy efficiency

Questions Related to energy efficiency

The power of a heart which pumps $5\times{10}^{3}cc$ of blood per minute at a pressure of $120mm$ of mercury ($g=10m{s}^{-2}$ and density of $Hg=13.6\times{10}^{3}kg/m$) is

energy efficiency energy transformations and energy transfers physics

  1. $1.36W$

  2. $13.6W$

  3. $0.136W$

  4. $136W$

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Correct Option: A

The work done during the process when 1 mole of gas is allowed to expand freely into vacuum is:

energy efficiency energy transformations and energy transfers physics

  1. zero

  2. +ve

  3. -ve

  4. either of these

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Correct Option: A

A man weighing 60 kg lifts a body of 15 kg to the top of a building 10 m high in 30 minutes. His efficiency is:

energy efficiency energy transformations and energy transfers physics

  1. 10%

  2. 20%

  3. 30%

  4. 40%

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Correct Option: B
Explanation:

Here, a man weighing 60 kg lifts a body of 15 kg to the top of a building 10 m high in 30 minutes. initially, while lifting the body(doing work) the power is 
$P _i = \dfrac{mgh}{t}$

$P _i = \dfrac{(60+15)(10)(10)}{(30)(60)}$

$P _i = \dfrac{7500}{1800}$

After reaching to the top the power is

$P _f = \dfrac{mgh}{t}$

$P _f = \dfrac{(15)(10)(10)}{(30)(60)}$

$P _f = \dfrac{1500}{1800}$

The efficiency of the man is the ratio of final power to the initial one
$\eta = \dfrac{P _f}{P _i}$

$\eta = \dfrac{\dfrac{1500}{1800}}{\dfrac{7500}{1800}} \times 100$ 

$\eta = \dfrac{1}{5} \times 100$ 

$\eta = 20$%

A motor has an electrical input of $30 kJ$ and is used to raise $100 kg$ load to a height of $25 m$ when fired to a crane winch. What is the efficient of winch ? ($g = 10 \ ms^{-1}$)

energy efficiency energy transformations and energy transfers physics

  1. $0.75 %$

  2. $83.3 %$

  3. $75 %$

  4. $17.5 %$

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Correct Option: B

A machine which is 75% efficient, uses 12 J of energy in lifting 1 kg mass through a certain distance. The mass is then allowed to fall through the same distance. The velocity at the end of its fall is:

energy efficiency energy transformations and energy transfers physics

  1. $\sqrt{12} $ m/s

  2. $\sqrt{18} $ m/s

  3. $\sqrt{24} $ m/s

  4. $\sqrt{32} $ m/s

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Correct Option: B
Explanation:

Efficiency = 75%, Input energy = 12 J
$\therefore \displaystyle \frac{75}{100} = \frac{\text{Output energy}}{\text{Input energy}}$
$\Rightarrow $ Output energy $= \displaystyle \frac{75}{100} \times 12 = 9 J$
$\therefore$ P.E. of the mass = 9 J
At the end of the fall it will be converted to K.E.
$\therefore \displaystyle \frac{1}{2} mv^2 = 9$
$\Rightarrow \displaystyle \frac{1}{2} \times 1 \times v^2 = 9$
$\Rightarrow v^2 = 18$
$\Rightarrow v = \sqrt{18} m/s$

An installation consisting of an electric motor driving a water pump left $75 L$ of water per second to a height of $4.7 m$. If the motor consumes a power of $5 kW$, then the efficiency of the installation is

energy efficiency energy transformations and energy transfers physics

  1. $39$%

  2. $69$%

  3. $93$%

  4. $96$%

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Correct Option: B
Explanation:

Power consumed by motor$5kW= 5 \times 10^3 W= 5000W$

power used i lifting water = $\dfrac{mgh}{t}=7.5 \times 9.8 \times 4.7= 3454.5 W$
Efficiency = $\dfrac{\text{Power used}}{\text{Power consumed}} \times 100$% = $\dfrac{3454.5}{5000} \times 100$% = 69 %

A man of 60 kg gains 1000 cal of heat by eating 5 mangoes. His efficiency is 56%. To what height he can jump by using this energy?

energy efficiency energy transformations and energy transfers physics

  1. 4m

  2. 20 m

  3. 078 m

  4. 0.2 m

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Correct Option: C