Question

If x times momentum is work find dimension of x

Answer 1

Hope it helps you............

Answer 2

Concept:

We will use the concept of units and dimensions. The study of the relationship between physical quantities with the help of dimensions and units of measurement is termed dimensional analysis.

Given:

x times momentum is work

Find:

We are asked to fin d the dimension of x

Solution:

As we know the dimension of momentum = mass ×velocity

mass = [M¹ L⁰ T⁰]

velocity = [M⁰ L¹ T⁻¹]

∴ momentum = [M¹ L¹ T⁻¹]

Work (W) = Force × Displacement

The dimensional formula of Force is [ M¹ L¹ T⁻²] ,  

Displacement= [M⁰ L¹ T⁰]

∴dimensional formula of work = [M¹ L² T⁻²]

According to question,

x(momentum)= work

x.  [M¹ L¹ T⁻¹]  = [M¹ L² T⁻²]

∴x = [M⁰ L¹ T⁻¹]

Hence the dimension of x will be [M⁰ L¹ T⁻¹]

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