Question

if x times linear momentum is kinetic energy then the dimensional formula of x

Answer 1

Given : x times linear momentum is kinetic energy  

To Find  :  the dimensional formula of x

Solution:

x times linear momentum is kinetic energy  

x  = kinetic energy   / Linear momentum

kinetic energy = (1/2) mv²

Linear momentum   = mv

kinetic energy   / Linear momentum   =  (1/2) mv² / mv

= v/2

x = v/2

Hence Dimensional formula of x  is same as of velocity

velocity = Displacement / time   = L/T  

M⁰L¹T⁻¹

Dimensional formula of x  M⁰L¹T⁻¹

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Answer 2

Given:

x times linear momentum is kinetic energy.

To find:

Dimensional Formula of x ?

Calculation:

• Let linear momentum be P , kinetic energy be KE.

$\rm \: x \times P = KE$

$\rm \implies \: [x] \times [P] = [KE]$

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

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

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

So, dimensional formula of [x] is :

$\boxed{ \bf \: [x] = [ L{T}^{ - 1} ]}$