Question

Is the equation a=v^2/r dimensionally correct?

Answer 1

Yes, the equation a=v^2/r is dimensionally correct.

Step-by-step explanation:

The dimensions of acceleration (a) are distance/time^2, the dimensions of velocity (v) are distance/time, and the dimensions of radius (r) are distance.

When we substitute these dimensions into the equation a=v^2/r, we get:

a = (distance/time)^2 / distance

Simplifying, we get:

a = distance^2 / time^2 / distance

a = 1 / time^2

Therefore, the dimensions of both sides of the equation are the same, which confirms that the equation is dimensionally correct.

Answer 2

No, the equation a=v^2/r is not dimensionally correct. This can be seen by breaking down the dimensions of each term in the equation.

The dimension of acceleration (a) is length/time^2 (L/T^2).

The dimension of velocity (v) is length/time (L/T).

The dimension of radius (r) is length (L).

Substituting these dimensions into the equation, we get:

L/T^2 = (L/T)^2 / L

Simplifying this expression, we get:

L/T^2 = L/T^2

This means that the dimensions on both sides of the equation are equal and therefore the equation is dimensionally correct.