Question

P=(b-x^2)÷at find ratio of dimenshion of a&b

Answer 1

: Is it p = b - (x^2)/at
then, see that power=work/time = (force*displacement)/time,
so, its unit is the same as that of
mass*acceleration*displacement/time,
so, its unit is
kg [m/(s^2)] m/s
= kg(m^2)/(s^3)
kg=kilogram,
m=meter
s=second,
its dimensional formula is [M(L^2)(S^(-3))]
and as you know that in an equation the left side and right side have same dimensions,
and as b and (x^20/at are separated by a subtraction sign, so
b has same dimensions as power, and (x^2)/at has same dimensions as p,
So, dimensions of (x^2)/at are kg(m^2)/(s^3)
and as the dimensions of x^2 is m^2, and that of t is s
so, dimensions of 'a' is the dimensions of (x^2)/pt
so, dimensions of 'a' is [M^(-1) L^(0) T^2]

Hope it helps