Question

The dimensions of kinetic energy is-
1. [M¹L¹T²]
2. [M1L2T^-2]
3. [M2L1T^-2]
4. [M^-1L1T2]

Answer 1

Correct Answer - Option 2 : [M1L2T^-2]

The correct answer is option 2) i.e. [M1L2T^-2]

CONCEPT:

• The dimensional formula is used to express any physical quantity in terms of fundamental quantities.
• Fundamental quantity: A quantity that can be measured is called a physical quantity. 
  • Fundamental quantities are those which cannot be expressed or measured in terms of other physical quantities. 
  • The SI system has seven fundamental quantities i.e. time, length, mass, electric current, thermodynamic temperature, amount of substance, and luminous intensity. 

The seven fundamental quantities along with their dimensions are as follows:

Fundamental quantity	Dimension
Time	T
Mass	M
Electric current	A
Thermodynamic temperature	K
Amount of substance	mol
Luminous intensity	cd
Length	L

EXPLANATION:

• ​Kinetic energy is the energy possessed by a moving object. 

Mathematically, kinetic energy (KE) is expressed as:

\(\Rightarrow KE=\frac{1}{2} mv^2\)

Where m is the mass of the object and v is the velocity of the object.

• Dimension of mass = [M¹]
• Dimension of velocity = [L¹T^-1]
• Thus, dimensions of kinetic energy = [M1][L1T-1]² = [M1L2T-2]