Unit And Dimensions - NEET Physics Questions
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Unit And Dimensions

Question 21: easy

Which of the following is a dimensional constant?

[1995]

1. Relative density
2. Gravitational constant
3. Refractive index
4. Poisson ratio
View Answer

A dimensional constant is a physical constant with dimensions. The Gravitational constant \(G\) is a dimensional constant with dimensions \(M^{-1}L^3T^{-2}\).

Question 22: easy

The dimensions of \(RC\) is:

[1995]

1. Square of time
2. Square of inverse time
3. Time
4. Inverse time
View Answer

The product \(RC\) represents the time constant of an \(RC\) circuit, and its dimension is time, \(T\).

Question 23: easy

Which of the following has the dimensions of pressure?

[1994,90]

1. \(MLT^{-2}\)
2. \(ML^{-1}T^{-2}\)
3. \(ML^{-2}T^{-2}\)
4. \(M^{-1}L^{-1}\)
View Answer

Pressure is defined as Force per unit Area. Its dimensions are \(MLT^{-2} / L^2 = ML^{-1}T^{-2}\).

Question 24: moderate

The dimensional formula of permeability of free space \(\mu_0\) is

[1991]

1. \(MLT^{-2}A^{-2}\)
2. \(M^0L^{-1}T\)
3. \(M^0LT^{-1}A^2\)
4. None of these
View Answer

From Ampere's law, the dimensions of permeability of free space \(\mu_0\) are derived as \(MLT^{-2}A^{-2}\).

Question 25: moderate

According to Newton, the viscous force acting between liquid layers of area \(A\) and velocity gradient \( \Delta v / \Delta z \) is given by \(F = -\eta A (\Delta v / \Delta z)\), where \(\eta\) is constant called coefficient of viscosity. The dimensional formula of \(\eta\) is:

[1990]

1. \(ML^{-2}T^{-2}\)
2. \(ML^0T^0\)
3. \(ML^2T^{-1}\)
4. \(ML^{-1}T^{-1}\)
View Answer

From the formula \(F = -\eta A (\Delta v / \Delta z)\), the dimension of \(\eta\) is \(F / (A \cdot (\Delta v / \Delta z)) = [MLT^{-2}] / ([L^2] \cdot [T^{-1}]) = [ML^{-1}T^{-1}]\).

Question 26: moderate

Which of the following quantities, which one has dimensions different from the remaining three?

[1989]

1. Energy per unit volume
2. Force per unit area
3. Product of voltage and charge per unit volume
4. Angular momentum
View Answer

Energy per unit volume, force per unit area, and product of voltage and charge per unit volume all have dimensions \(ML^{-1}T^{-2}\). Angular momentum has dimensions \(ML^2T^{-1}\), which is different.

Question 27: easy

Dimensional formula of self inductance is:

[1989]

1. \(MLT^{-2}A^{-2}\)
2. \(ML^2T^{-1}A^{-2}\)
3. \(ML^2T^{-2}A^{-2}\)
4. \(ML^2T^2A^{-1}\)
View Answer

The energy stored in an inductor is \(U = \frac{1}{2}LI^2\). Therefore, the dimensions of self-inductance \(L\) are \(U/I^2 = [ML^2T^{-2}]/[A^2] = [ML^2T^{-2}A^{-2}]\).

Question 28: easy

The dimensional formula of torque is:

[1989]

1. \(ML^2T^{-2}\)
2. \(MLT^{-2}\)
3. \(ML^{-1}T^{-2}\)
4. \(ML^{-2}T^{-2}\)
View Answer

Torque is calculated as Force \(\times\) perpendicular distance. So its dimensions are \([MLT^{-2}] \times [L] = [ML^2T^{-2}]\).

Question 29: easy

If \(C\) and \(R\) denote capacitance and resistance, the dimensional formula of \(CR\) is:

[1988]

1. \(M^0L^0T^1\)
2. \(M^0L^0T^0\)
3. \(M^0L^0T^{-1}\)
4. Not expressible in terms of MLT
View Answer

The product \(CR\) is the time constant of an RC circuit. Its dimension is time, \(T\), which can be written as \(M^0L^0T^1\).

Question 30: easy

The dimensional formula of angular momentum is:

[1988]

1. \(ML^2T^{-2}\)
2. \(ML^{-2}T^{-1}\)
3. \(MLT^{-1}\)
4. \(ML^2T^{-1}\)
View Answer

Angular momentum is defined as \(L = r \times p\), where \(r\) is distance and \(p\) is linear momentum. Its dimensions are \([L][MLT^{-1}] = [ML^2T^{-1}]\).