Question

24. If in the following equations, s is distance and t is time,
find the dimensional formula of A,B,C and D.
s = At, s = Bt^2, s =C sin Dt
​

Answer 1

☆Remember:

》Standard way to represent:

• Length/distance - L
• time - T

》angle is a dimensionless quantity.

☆ Solution

1) s=At

• [L]¹ = A[T]¹

• $\rm A= [L]¹[T]^{-1}$--------☆

2) s= Bt²

• [L]¹ = B[T]²----------☆

•$\rm B = [L]¹[T]^{-2}$

3) s= C sin(Dt)

》Dt is angle, it will be dimensionless.

• D[T]¹ = [L]⁰[T]⁰

• $\rm D = [T]^{-1}$---------☆

》As sinDt is dimensionless C will be compared with s.

• s = C

$\rm C = [L]¹$----------☆