Explanation:

Momentum is defined as the product of mass and velocity of an object. It is a vector quantity and is denoted by the symbol P.

Formula: P = mv

where m is the mass of the object and v is its velocity.

Given, P = √a/b v^2

To find the dimensional formula of ab^-2, we need to first simplify the given equation.

Squaring both sides of the equation, we get:

P^2 = a/b v^2

Substituting the value of P from the formula of momentum, we get:

(mv)^2 = a/b v^2

Simplifying, we get:

m^2v^2 = ab^-1 v^2

Cancelling v^2 on both sides, we get:

m^2 = ab^-1

Taking the dimensional formula of m as [M], we get:

[M]^2 = [A][B]^-1

where [A] and [B] are the dimensional formula of a and b respectively.

To find the dimensional formula of ab^-2, we need to solve for [A] and [B].

Multiplying both sides of the equation by [B]^2, we get:

[M]^2[B]^2 = [A][B]

Dividing both sides of the equation by [B], we get:

[M]^2[B] = [A]

Substituting the dimensional formula of m as [M], we get:

[M]^2[B] = [A] = [M]^2[B]^-1

Multiplying both sides of the equation by [B], we get:

[M]^2[B]^2 = [M]^2

Cancelling out [M]^2 on both sides, we get:

[B]^2 = 1

Taking the square root of both sides, we get:

[B] = ±1

Since [B] cannot be negative, we take [B] = 1.

Substituting the value of [B] in the equation [M]^2[B] = [A], we get:

[A] = [M]^2

Therefore, the dimensional formula of ab^-2 is [M]^2.

Conclusion:

In conclusion, the dimensional formula of ab^-2 is [M]^2. The above explanation shows how to derive this formula using the given equation and the formula of momentum. It is important to note that dimensional analysis is a powerful tool that can be used to derive the units of any physical quantity.

I think it is M2L2T_2