If linear momentum p, acceleration a, time t, are taken to be fundamental quantities, then dimensional formula of mass is?

Question

Answer

Dimensional Formula of Mass

When we say that linear momentum p, acceleration a, and time t are fundamental quantities, we mean that they cannot be expressed in terms of other physical quantities. Mass, on the other hand, can be expressed in terms of these fundamental quantities.

Explanation

The dimensional formula of a physical quantity is a way of expressing the physical quantity in terms of the fundamental quantities. In other words, it is a way of expressing a physical quantity in terms of its dimensions. The dimensions of a physical quantity are the powers to which the fundamental quantities must be raised to express the physical quantity in terms of those quantities.

The dimensional formula of mass can be derived using the equation:

p = m * v

Where p is the linear momentum, m is the mass, and v is the velocity.

Linear momentum has the dimensional formula:

[p] = [m][v]

Acceleration has the dimensional formula:

[a] = [v]/[t]

Substituting the value of [v] from the equation for linear momentum, we get:

[a] = [p]/([m][t])

Therefore, the dimensional formula of mass can be derived as:

[m] = [p]/([a][t])

Substituting the dimensions of linear momentum and acceleration, we get:

[m] = [MLT^-1]/([LT^-2][T]) = [M^1L^1T^-2T^-1] = [M^1L^1T^-1]

Conclusion

The dimensional formula of mass is [M^1L^1T^-1]. This means that mass has dimensions of one unit of mass, one unit of length, and negative one unit of time.

Answer

[M]=[F]/[a]
=[p]/[a][t]
[M]=p^1*a^-1*t^-1

Answer

P^1a^-1t^-1

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