Identify the dimensions of v from the table above: Identify the dimensions of a from the table above and multiply by the dimensions of t: Therefore,
v = at is dimensionally correct
because we have the same dimensions on both sides.
Is this dimensionally correct?
An equation in which each term has the same dimensions is said to be dimensionally correct
. All equations used in any science should be dimensionally correct. The only time you’ll encounter one which isn’t is if there is an error in the equation.
What is the dimensional formula of V?
| Physical Quantity Dimensional Equation | Force (F) F = [M L T-2] | Power (P) P = [M L2 T-3] | Velocity (v) v = [M L T-1] | Density (D) D = [M L3 T0] |
|---|
Which of the following is dimensionally correct U V at?
u=v−at , u is initial velocity, v is final velocity, a is acceleration and t is time. ⇒
LT−1=LT−1−(LT−1)
. Hence it is dimensionally correct.
Is V V at dimensionally correct?
Note that v and v0 are velocities and that a is an acceleration. Write the dimension of each term. The dimensions of both the sides are the same. Thus,
the equation is dimensionally consistent
.
Is MGH 1 2mv2 dimensionally correct?
Both sides are dimensionally the same, hence the equations
12mv2 = mgh is dimensionally correct
.
Is v2 U 2as dimensionally correct?
Now s = distance and distance is measured in meter or centimeter. Now as we know that the dimension is independent of scaling so the dimension of 2as is
[L2T−2]
. Hence the given relation is accurate.
Which equations is dimensionally correct?
Hence, the given equation
y=(2m)cos(kx)
is dimensionally correct.
Which is dimensionally correct?
so, dimensionally,
pressure = energy per unit volume
. option (B) is correct. … so, Dimensionally, pressure ≠ force per unit volume per unit time.
Are all equations dimensionally correct?
Units and Measurement
This statement is wrong. A dimensionally correct equation may or may not be numerically correct. Therefore
the equation is dimensionally correct
. The angle subtended by an arc of length l, circle of radius r, at the center is given by t/r.
How many dimensions are there?
The world as we know it has
three dimensions of space
—length, width and depth—and one dimension of time. But there’s the mind-bending possibility that many more dimensions exist out there. According to string theory, one of the leading physics model of the last half century, the universe operates with 10 dimensions.
What is the dimensional velocity?
| Quantity Dimension Unit | velocity [L T – 1 ] meter per second | acceleration [L T – 2 ] meter per second squared | density [M L – 3 ] kilogram per cubic meter | force [M L T – 2 ] newton |
|---|
What is v2 u2 2as?
Key Point. The equations of motion with constant acceleration: v = u + at v2 = u2 +
2as s = ut + 1 2 at2
where u = initial speed, v = final speed, a = acceleration, t = time, s = distance travelled. 6. The formula for kinetic energy.
Which formula is dimensionally incorrect?
u=v−
at , u is initial velocity, v is final velocity, a is acceleration and t is time. ⇒LT−1=LT−1−(LT−1) . Hence it is dimensionally correct.
What are the three limitations of dimensional analysis?
Dimensional Analysis can’t derive relation or formula if a physical quantity depends upon more than three factors having dimensions. It can’t derive
a formula containing trigonometric function, exponential function, and logarithmic function
and it can’t derive a relation having more than one part in an equation.
How do you know if an equation is dimensionally consistent?
The only way in which this can be the case is if all laws of physics are dimensionally consistent: i.e., the quantities on the left- and right-hand sides of the equality sign in any given law of
physics must have the same dimensions
(i.e., the same combinations of length, mass, and time).
