Question

Statement -1: Kinetic energy can be divided by volume and
Statement -2: Dimensions of kinetic energy and volume are different
A) Statement -1 is True Statement -2 is True;
Statement -2 is a correct explanation for Statement -1
B) Statement -1 is True Statement -2 is True;
Statement -2 is NOT a correct explanation for Statement -1
C) Statement -1 is True Statement -2 is False.
D) Statement -1 is False Statement -2 is true.

Answer 1

To find out the question related with dimensional formula first of all try to derive the dimensional formula of the given quantities in the question and then evaluate them. By comparing the dimensional formula of kinetic energy with the dimensional formula of volume, we can find out whether they are the same or different.

Complete step by step solution: Divisions of two quantities having different dimensions is possible. Therefore, statement -1 is true.
Dimensional formula for Kinetic energy is ${\text{[M}}{{\text{L}}^{\text{2}}}{{\text{T}}^{{\text{ - 2}}}}{\text{]}}$
The SI unit of kinetic energy is joule represented by J.
Formula for volume is given by
$l\times b\times h$
Where l = length
b = breadth
and h = height
Dimensional formula for length (l) is [L]
Dimensional formula for breadth (b) is [L]
Dimensional formula for height (h) is [L]
Dimensional formula for volume is [L3]
So, dimensional formula for volume is ${\text{[}}{{\text{M}}^{\text{0}}}{{\text{L}}^{\text{3}}}{{\text{T}}^{\text{0}}}{\text{]}}$
The SI unit of volume is m3.
Thus, the dimensional formula for kinetic energy is ${\text{[M}}{{\text{L}}^{\text{2}}}{{\text{T}}^{{\text{ - 2}}}}{\text{]}}$and dimensional formula for volume is ${\text{[}}{{\text{M}}^{\text{0}}}{{\text{L}}^{\text{3}}}{{\text{T}}^{\text{0}}}{\text{]}}$. Here, it is clear that dimensional formula for volume is different to that of the kinetic energy.
So, statement -2 is correct but it is not a valid explanation for statement -2.

Therefore, option (B) is the correct choice.

Note: Dimensions are denoted with square brackets. The dimensional formula of length, mass, time, electric current, thermodynamic temperature, luminous intensity and amount of substance are [L], [M], [A], [K], [Cd] and [mol] respectively. These are the quantities called primary quantities from which all other secondary quantities can be obtained.