Question

find the dimension of a×b in the
given equation P = a/bx -t^2/b

where. P is the powere, x is the
distance & t in. time.​

Answer 1

Answer:-

$a \times b = T^2$

Given :-

$P = \dfrac{a}{bx}-\dfrac{t^2}{b}$

To find:-

Dimension of a × b.

Solution:-

Dimensional formula of power :-

$\mathsf{P = [ML^2T^{-2}]}$

• By using principal of homeginity.

→$P = \dfrac{a}{bx}-\dfrac{t^2}{b}$

→$P = a$

→$a = [ML^2 T^{-2}]$

Now,

→$P = \dfrac{t^2}{b}$

→$b[ML^2T^{-2}] = T^2$

→$b = \dfrac{T^2}{ML^2T^{-2}}$

→$b = M^{-1}L^{-2}T^{2+2}$

→$b = [M^{-1}L^{-2}T^{4}]$

$a \times b$

→$(ML^{2}T^{-2} \times M^{-1}L^{-2}T^{4} )$

→$( M^{1-1}L^{2-2}T^{-2+4} )$

→$T^2$

hence,

Dimension formula of a × b is $T^2$