Question

The dimension of calorie are:
$\begin{aligned} & \text{A}\text{. M}{{\text{L}}^{2}}{{\text{T}}^{-2}} \\\ & \text{B}\text{. ML}{{\text{T}}^{-2}} \\\ & \text{C}\text{. M}{{\text{L}}^{2}}{{\text{T}}^{-1}} \\\ & \text{D}\text{. M}{{\text{L}}^{-2}}{{\text{T}}^{-1}} \\\ \end{aligned}$

Answer 1

Convert the derived physical quantities into fundamental physical quantities. A calorie is a unit of energy. So, the dimension of calories is the same as that of the dimension of energy. Express the energy in terms of the fundamental physical quantities. Then find the dimension of each fundamental quantity to find the required dimension.

Complete step-by-step solution:
All the derived physical quantities can be expressed in terms of the fundamental quantities. The derived units are dependent on the 7 fundamental quantities. Fundamental units are mutually independent of each other.
The dimension of a physical quantity is the power to which the fundamental quantities are raised to express that physical quantity.
A calorie is a unit of energy used in the nutrition industry. So, the dimension of calories will be the same as the dimension of energy.
We can simply find the energy by expressing it as
$E=\dfrac{1}{2}m{{v}^{2}}$
Where m is the mass of the object and v is the velocity of the object.
Dimension of mass is $M{{L}^{0}}{{T}^{0}}$
Again, dimension of velocity can be given as, ${{M}^{0}}L{{T}^{-1}}$
So, we can express the dimension of energy as,
$\begin{aligned} & E=\dfrac{1}{2}m{{v}^{2}} \\\ & E=\left[ M{{L}^{0}}{{T}^{0}} \right]\times {{\left[ {{M}^{0}}L{{T}^{-1}} \right]}^{2}} \\\ & E=\left[ M{{L}^{2}}{{T}^{-2}} \right] \\\ \end{aligned}$
So, the correct option is (A).

Note: Don’t try to remember the dimensional formula. You may get confused. Always express the derived quantities in terms of the fundamental quantities and you will get the dimension of quantities. We can also find the dimension of energy by expressing it as the product of force and distance or from the expression of kinetic energy or potential energy. We can use any one of the above mathematical expressions to find the dimension of energy.