Question

A new system of units is proposed in which unit of mass is α kg, unit of length β m and unit of time γ s. how much will 5 J measure in this new system?

Answer 1

Dimension of energy = [ML²T^-2],

n₁u₂= n₁u₁

_{\(n_2=n_1\frac{u_1}{u_2}\)}

_{\(=n_1[\frac{M_1}{M_2}]^1[\frac{L_1}{L_2}]^2[\frac{T_1}{T_2}]^{-2}\)}

Given:

n₁= 5 J 

M₂ = α kg, 

M₁ = 1 kg, 

L₂= β m, 

T₁ = 1 sec, 

T₂ = γ s, 

L₁ = 1m,

∴ n₂ = 5J \([\frac{1kg}{αkg}]^1[\frac{1m}{βm}]^2[\frac{1sec}{γsec}]^{-2}\)

n₂ = 5J[α⁻¹β⁻²γ²]

New system = \(\frac{5γ^2}{αβ^2}J\)