Question

the velocity of a body is given by v=A+B/(C-S) whers S is the displacement. The dimensions of B are?​

Answer 1

Answer:

(L-2T-1) IS THEDIMENSIONS OF B

Answer 2

Answer:

The dimensions of B are $L^{2} T^{-1}$

Explanation:

Given the velocity of the body is V= $\frac{A+B}{C-S}$,  S is displacement.

According to the principle of homogeneity:

• Algebraic operators can be applied between the quantities of the same dimensions.
• if A=B then the dimensions of the A and B are the same

with the above-stated rules, we can conclude that

1. dimension of C is equal to S
2. Velocity (V) ' s dimension is equal to the RHS side's dimension as a whole

S =[L] ⇒ C= [L]  (L defines the length)

We know that velocity dimensions is $LT^{-1}$

C-S ⇒ represents the Length dimension

A+B ⇒ hence it should have dimensions as $L^{2} T^{-1}$ .

so that   $L T^{-1}=\frac{L^{2} T^{-1}}{L}$

therefore, through the principle of homogeneity, we can conclude that dimensions of B are $L^{2} T^{-1}$.