Statement (A): Dimensional formula for area is[M⁰L²T⁰]
Statement (B) : Dimensional formula for speed is [M⁰L¹T^-1]

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Both A and B are true

Both A and B are false

A is true but B is false

A is false but B is true

answer is A.

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Detailed Solution

The dimensional formula of a physical quantity is a way to represent it in terms of the basic dimensions of mass [M], length [L], and time [T]. Let us analyze the given statements:

Statement (A): Dimensional formula for area is [M⁰L²T⁰].

Area refers to the extent of a two-dimensional surface and is calculated as the product of two lengths (e.g., length × breadth for a rectangle).
Since the unit of length is L, the dimensional formula for area becomes L × L = L².
There is no involvement of mass or time in the calculation of area, so the powers of M and T are zero.
Thus, the area dimensional formula is [M⁰L²T⁰], which is correct.

Statement (B): Dimensional formula for speed is [M⁰L¹T^-1].

Speed is defined as the distance traveled per unit time. Its formula is: Speed = Distance / Time.
The dimensional formula for distance is [L], and for time, it is [T].
Dividing L by T, the dimensional formula for speed becomes [L¹T^-1].
Like area, speed does not depend on mass, so the power of M is zero.
Therefore, the dimensional formula for speed is [M⁰L¹T^-1], which is also correct.