Question

If x times the linear momentum is work then the dimensional formula of x is

Answer 1

dimensional formula of x is LT-1

work =X*P

so dimension of X =ML2T-2/MLT-1

=LT-1

Answer 2

Given:

x times Linear momentum = Work

To find:

Dimensional formula of x ?

Calculation:

$x \times P = work$

• Now, expressing the dimensions of each quantities:

$\implies [x]\times [P] = [work]$

$\implies [x]\times [M \times L{T}^{ - 1} ] = [M{L}^{2} {T}^{ - 2} ]$

• M is mass, L is length, T is time

$\implies [x]\times [M L{T}^{ - 1} ] = [M{L}^{2} {T}^{ - 2} ]$

$\implies [x] = \dfrac{[M{L}^{2} {T}^{ - 2} ]}{[M L{T}^{ - 1} ]}$

$\implies [x] = [L {T}^{ - 1} ]$

So, dimension of x is [LT^(-1)]