Question

6. Find the dimensions of a / b in the equation: F=a √x +bt2 , where F is force, x is distance and t is time.

Answer 1

hope it helps........

Answer 2

Answer:

The dimensions of the ratio of a and b is $[L^{-\frac{1}{2}}T^2]$.

Explanation:

Given that,

$F =a\sqrt{x}+bt^2$

Where, F = force

x = distance

According to principle of homogeneity,

The dimension of every term on right hand side should be same as that on Left hand side.

The dimension formula of a

$F = a\sqrt{x}$

$a = \dfrac{F}{\sqrt{x}}$

Now, write the dimension formula in the equation (I)

$a = \dfrac{[MLT^{-2}]}{[L^{\frac{1}{2}}]}$

$a = [ML^{\frac{1}{2}}T^{-2}]$

the dimension formula of b

$F = bt^2$

$b = \dfrac{F}{t^2}$....(II)

Now, write the dimension formula in the equation (II)

$b = \dfrac{[MLT^{-2}]}{[T^{2}]}$

$b= [MLT^{4}]$

The dimension of a and b is

$\dfrac{a}{b}=\dfrac{ [ML^{\frac{1}{2}}T^{-2}]}{[MLT^{4}]}$

$\dfrac{a}{b}=[L^{-\frac{1}{2}}T^2]$

Hence, The dimensions of the ratio of a and b is $[L^{-\frac{1}{2}}T^2]$.