Question

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Answer 1

Answer:

option b) B represents acceleration

Explanation:

Law of Homogeneity of Dimensions :

• It states that the dimensions of all the terms must be same on both sides of the equation.
• The terms separated by '+' or '–' have the same dimensions.

The given equation is

 $\tt v=\sqrt{AB}+Bt+\dfrac{C}{D+t}$

The dimensions of √AB , Bt and C/D+t must have the same dimensions as that of the speed 'v'.

[v] = [√AB] = [Bt] = [C/D+t]

• The dimension of speed, v : [v] = [LT⁻¹]

• The dimension of time, t : [t] = [T]

From the principle of homogeneity,

[v] = [Bt]

[LT⁻¹] = [B] [T]

[LT⁻¹]/[T] = [B]

[B] = [LT⁻²]

[B] has the same dimension as that of acceleration.

⇒  B represents acceleration

Similarly,

[D] has the same dimension as that of time.

[D] = [T]

⇒ D represents time

[v] = [C/D+t]

[LT⁻¹] = [C]/[T]

[LT⁻¹] [T] = [C]

[C] = [L]

C has the same dimension as that of length

⇒ C represents distance

$\bf [v]=[\sqrt{AB}]$

[v]² = [AB]

[LT⁻¹]² = [AB]

[L²T⁻²] = [A] [B]

[L²T⁻²] = [A] [LT⁻²]

[L²T⁻²] / [LT⁻²] = [A]

[A] = [L]

A has the same dimension as that of length

⇒ A represents distance