In a new system the unit of mass is α kg, unit of length is β m and unit of times of γ s. The value of 1 J in this new system is :-

Question

In a new system the unit of mass is α kg, unit of length is β m and unit of times of &gamma; s. The value of 1 J in this new system is :- (A) (&gamma;2/α β2) (B) (&gamma; α/β2) (C) α β &gamma; (D) α &gamma;2 / β2

Tardigrade Admin · Accepted Answer

n 2= n 1 [( M 1/ M 2)]1[( L 1/ L 2)]2[( T 1/ T 2)]-2 =1 × (1/α) ×((1/β))2 ×((1/&gamma;))-2 =&gamma;2 / α β2

Q. In a new system the unit of mass is $α k g$ , unit of length is $β m$ and unit of times of $γ s$ . The value of $1 J$ in this new system is :-

$\frac{γ ^{2}}{α β ^{2}}$

$\frac{γ α}{β ^{2}}$

$α β γ$

$α γ^{2} / β^{2}$

$n_{2} = n_{1}$
$[\frac{M _{1}}{M _{2}}]^{1} [\frac{L _{1}}{L _{2}}]^{2} [\frac{T _{1}}{T _{2}}]^{- 2}$
$= 1 \times \frac{1}{α} \times (\frac{1}{β})^{2} \times (\frac{1}{γ})^{- 2}$
$= γ^{2} / α β^{2}$

Q. In a new system the unit of mass is αkg, unit of length is βm and unit of times of γs. The value of 1J in this new system is :-

αβ2γ2​

β2γα​

αβγ

αγ2/β2