Question

What is the dimension of a new quantity named “CHIGS” if it depends only on velocity of an object and mass of object.
i. CHIGS is proportional to mass of object keeping velocity constant.
ii. CHIGS is proportional to the kinetic energy of an object keeping mass constant.
A. Question can be solved by information $\left( i \right)$ only.
B. Questions can be solved by information $\left( ii \right)$ only.
C. Questions can be solved by information $\left( i \right)$ and $\left( ii \right)$ in combined form only.
D. Questions can be solved independently by information $\left( i \right)$ and $\left( ii \right)$.

Answer 1

Hint: The dimension of a quantity can be defined as the expression which shows the powers of the fundamental units that need to be raised so as to get the unit of the dimensional quantity. The dimensional formula of a particular quantity is written in square brackets with proper symbols and their appropriate powers.


Complete step-by-step solution:
In the question, we are given that the dimension of the new quantity depends on both velocity and mass of an object. Next, we are given in the first option that CHIGS is proportional to mass of object keeping velocity constant and in the other option we are given that CHIGS is proportional to kinetic energy of object keeping mass constant. If we need to find the dimensions of the quantity then we need to consider all the independent variables on which the quantity would depend. Thus, to find the dimension of the new quantity named “CHIGS” we would need both mass and velocity. We could get a relationship of “CHIGS” with velocity with the help of its kinetic energy if mass is kept constant and we could get a relationship of “CHIGS” with mass by keeping mass constant. Hence, the question can be solved by information $\left( i \right)$ and $\left( ii \right)$ in combined form only.
Thus, option $C$ is correct.

Note: The fundamental quantities that are generally used to define a quantity are mass, length, time, temperature, electric current, luminous intensity and amount of substance. These quantities that are seven in number are also known as the seven dimensions of the physical world.