Question

Derive the formula for kinetic energy of a particle having mass and velocity using dimensional analysis

Answer 1

Explanation:

Kinetic energy can be defined as the energy possessed by the body by virtue of its motion.

Mathematically,

Kinetic energy (K.E) = 1/2 [Mass (m) X Velocity (v)2]

Dimensional formula of Mass = M1L0T0

Dimensional formula of velocity= M0L1T-1

Putting the values in the above equation we get,

Dimensional formula of Kinetic energy (K.E) = M1L0T0 X ( M0L1T-1)2

Dimensional formula of Kinetic energy (K.E) = M1L0T0 X M0L2T-2

Dimensional Formula of Kinetic energy= M1L2T-2.

SI unit of Kinetic energy is Joule (J).

In the above equation ½ is a constant and constants do not affect the dimensional formula of any quantity.

Answer 2

$\huge\colorbox{orange}{Answer}$

.

Kinetic energy is one of the types of energy and it is defined as the energy in an object due to its virtue of motion. The dimension of kinetic energy will be the same as that of energy. Therefore, kinetic energy is measured in Joules (SI unit of energy) and its dimensional formula will be [M1L2T−2].