Question

For what minimum height, a block of ice has to be dropped in order that it may melt completely on hitting the ground:
A. $mgh$
B. $\dfrac{{mgh}}{l}$
C. $\dfrac{l}{g}$
D. $\dfrac{h}{{\lg }}$

Answer 1

Since in this question, we are dropping a block of ice from a particular height, so we will equate the gravitational potential energy with the product of the mass and latent heat of fusion. By resolving the expression, we will find the relation for the minimum height.

Formula Used:
The formula for the potential energy can be expressed as the product of the mass, acceleration due to gravity and the distance between the object and the ground. This can be expressed as:’
$\Rightarrow P.E. = mgh$
Where $m$ is the mass of the object, $g$ is the acceleration due to gravity and $h$ is the distance of the object from the ground.

Complete step by step answer:
We will write the expression for the potential energy of the block of ice.
$\Rightarrow P.E. = mgh$……(i)
Where $m$ is the mass of the object, $g$ is the acceleration due to gravity and $h$ is the distance of the object from the ground.
The energy absorbed by the ice block to completely melt is expressed as:
$\Rightarrow {\rm{Heat absorbed}} = m \times l$ ……(ii)
Where $l$ is the latent heat of fusion.
Now we will equate the potential energy and the heat absorbed by the ice by equating equation (i) and (ii). This can be expressed as:
$\Rightarrow mgh = m \times l\\\ \Rightarrow gh = l$
Om rearranging the above expression, we will get
$\Rightarrow h = \dfrac{l}{g}$
The minimum height should be $\dfrac{l}{g}$. Hence option C is the correct answer.

Note: Whenever ice melts, it absorbs a certain amount of heat. In this case, we have utilized the energy from the melting of ice. Hence, the gravitational potential energy converts into the latent heat of fusion.