If momentum P and velocity v are related as P=√a÷b+v2 then dimensional...
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.
If momentum P and velocity v are related as P=√a÷b+v2 then dimensional...
I think it is M2L2T_2
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