Question

A man of 60kg gains 1000 Cal of heat by eating 5 mangoes. His efficiency is 56%. To what weight can he jump by using this energy?
(A) 4 m
(B) 20 m
(C) 28 m
(D) 0.2 m

Answer 1

Hint: The efficiency is the ratio of output work to the input taken, since, the efficiency is 56% it means if 100 J of heat is given to a system then it gives an output of 56J and remaining is lost. We need to find how much height he can scale using the given input.

Complete step by step answer:
Mass of man, m= 60 kg
Heat input, H= 1000 C
We know 1 cal= 4.184 J
So 1000 cal= 4184 J
Using the formula, \[e=\frac{output}{input}\]
Efficiency is given in percentage, converting it into decimals, 0.56
So, \[0.56=\frac{output}{4184}\]
\[\begin{align}
  & 0.56=\frac{output}{4184} \\
 & =0.56\times 4184 \\
\end{align}\]
Output= 2343.04 J
Now while jumping in reaching maximum height h, this energy gets converted to gravitational potential energy
mgh=2343.04
h=\[\frac{2343.04}{9.8\times 60}=4m\]
so, the height reached is 4m. Hence, the correct option is (A)

Additional Information: A calorie is the amount of heat needed to raise the temperature of one gram of water by one degree Celsius. Usually, the energy that we get from food is measured in terms of this unit only. Our bodies store and burn calories as fuel. Counting calories is one way to monitor weight loss.

Note:Here we have assumed no loss of energy and there is a complete conversion of energy from one form to another but in real life, there is no process which is 100% efficient that there is a complete conversion of energy from one form to another without any loss.