Question

Using dimensional analysis, show that energy can be calculated from the following energy equations. Hint, in SI, here we want Joules.

(6 pts)

E = 1 2 mv2 (5)

E = mgh (6)

Answer 1

Step-by-step explanation:

1. The kinetic energy of any object is calculated as :

`E=(1)/(2)mv^2`...........(1)

Dimensional formula of energy,
`[E]=[ML^2T^(-2)]`

Dimensional formula of mass is
`[M]`

Dimensional formula of velocity,
`[v]=[LT^(-1)]`

`[ML^2T^(-2)]=(1)/(2)[M]([LT^(-1)])^2`

So,
`[ML^2T^(-2)]=[ML^2T^(-2)]`

LHS = RHS

2. The potential energy is given by :

`E=mgh`

Dimensional formula of mass is
`[M]`

Dimensional formula of g is
`[LT^(-2)]`

Dimensional formula of height is
`[L]`

Dimensional formula of energy,
`[E]=[ML^2T^(-2)]`

So,
`E=[M][LT^(-2)][L]`

So, LHS = RHS

Hence, this is the required solution.