Question

the energy E of a particle at position X at time t is given by E= a/t(b+x2), where a and b are constants. the dimensional formula of a is?​

Answer 1

Answer:

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Answer 2

Given: Energy of a particle at position X at time t is given by E = a/t(b+x²)

          a and b are constant.

To find: The dimensional formula of a

Solution:

• Dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measure (such as miles vs. kilometres, or pounds vs. kilograms).

• Since the energy has dimensional formula is [ ML²T⁻² ]

• Where M is the mass, L is te length, and T is the time period.

• Since x is the distance, from the rule of addition, two quantity can only be added if it has similar unit.

• Therefore, b has the dimensional formula of [ L² ]

Now, E = a/t(b + x²)

Putting the dimensional formula in the equation,

[ ML²T⁻² ] = a/[T][L²]

[ ML²T⁻² ] = a[T⁻¹][L⁻²]

a = [ML²T⁻²] / [T⁻¹][L⁻²]

a = [ML⁴T⁻¹]

Therefore, the dimensional formula of a is  [ML⁴T⁻¹].