Question

A body of mass $5\;kg$ falls from a height of $30\;m$. If all its mechanical energy is changed to heat, then the heat produced will be:
A. 350 cal
B. 150 cal
C. 60 cal
D. 6 cal

Answer 1

Recall that the mechanical energy possessed by a body by virtue of its position at a height is nothing but the gravitational potential energy. We are given that all of this is turned to heat. Thus, the heat produced is equal to the gravitational potential energy, which is a function of the mass and height of the body, and acceleration due to gravity. Use these deductions to arrive at the appropriate result. Also, remember that $1 cal = 4.2\;J$, since you might calculate the gravitational potential in joules.

Formula used:
Gravitational potential energy $U = mgh$
Work Energy theorem: $W_{net} = \Delta KE$

Complete step-by-step answer:
We know that gravitational potential energy is the energy an object possesses by virtue of its position in a gravitational field. This can be quantified as:
$U_{gravity} = mgh$, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the centre of mass of the object.
For a body at a height h, the mechanical energy it possesses is completely potential energy, which gets converted to kinetic energy as the body falls under the influence of gravity. But in the question, we are given that all the potential energy is changed to heat.
Then, according to the work-energy theorem, the net work done by the gravitational potential $W_{GP} = U_{gravity}$ will be equal to the amount of heat $Q$ generated.
$\Rightarrow W_{GP} = Q$
$\Rightarrow U_{gravity} = Q \Rightarrow mgh=Q$
$\Rightarrow Q = 5 \times 9.8 \times 30 = 1470\;J$
Now, we know that $1 cal = 4.2\;J$
$\Rightarrow Q = \dfrac{1470}{4.2} = 350\;cal$
Therefore, the correct option is A. 350 cal.

So, the correct answer is “Option A”.

Note: Remember that in general, when a body is released from a height under the influence of gravity, it possesses potential energy which gets translated into kinetic energy facilitating the motion of the body. The work done by the gravitational potential is equivalent to this change in kinetic energy of the body in accordance with the work-energy theorem, but it is only in this case that we assume that all the mechanical energy is converted to heat energy and not straight up kinetic energy. Therefore, remember to tweak the work-energy theorem to suit the context of the problem statement.