Question

A body of mass $5kg$ falls from a height of $30m$. If all its mechanical energy is lost into heat, then the heat produced will be
(A) $350{\text{ }}cal$
(B) $150{\text{ }}cal$
(C) $60{\text{ }}cal$
(D) ${\text{6 }}cal$

Answer 1

Hint
To solve this question, we need to find the total mechanical energy, which will be equal to the potential energy of the mass. Since all the mechanical energy is lost into heat, so heat produced will be equal to this energy.
The formula used in solving this question is
$\Rightarrow P.E. = mgh$, where $P.E.$ is the potential energy of a body of mass $m$ at a height $h$.
$\Rightarrow 1cal = 4.2J$

Complete step by step answer
As the body is falling from the given height, its potential energy at the topmost point is given by
$\Rightarrow P.E. = mgh$
According to the question, $m = 5kg$ and $h = 30m$
$\Rightarrow P.E. = 5(9.8)(30)$
$\therefore P.E. = 1470J$
As the body falls downwards, it starts gaining kinetic energy and losing potential energy.
Since there is no external force acting on the body except for the conservative gravitational force, the loss in potential energy at every point equals the gain in kinetic energy.
Therefore, the total mechanical energy of the body remains constant throughout the fall.
Hence, the total mechanical energy $E$ equals the initial potential energy of the body.
$\therefore E = 1470J$
Now, according to the question, all of this mechanical energy is lost into heat.
So the heat produced $H$ will be equal to the total mechanical energy of the body, which is given as
$\Rightarrow H = 1470J$
As the options have the energies in the unit of calories, we need to convert this energy into an equivalent amount of calories.
We know that $1cal = 4.2J$
Which means $1J = \dfrac{1}{{4.2}}cal$
Therefore, $1470J = \dfrac{{1470}}{{4.2}}cal$
Or, $H = 350cal$
Thus, the heat generated is equal to $350cal$
Hence the correct answer is option (A), $350cal$.

Note
Be careful while performing the conversion of units from $J$ to $cal$. It is a common confusion that whether the number $4.2$ is to be multiplied or divided while converting the units. To avoid this confusion, we should keep in mind that Joule is a smaller unit than calorie. So, the number $4.2$ should be divided.