Unit And Dimensions - NEET Physics Questions
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Unit And Dimensions

Practice Questions:
Question 51: moderate

The density of a material in CGS system of units is \(4\text{ g/cm}^3\). In a system of units in which unit of length is \(10\text{ cm}\) and unit of mass is \(100\text{ g}\), the value of density of material will be:

[2011 Mains]

 

1. \(0.4\)
2. \(40\)
3. \(400\)
4. \(0.04\)
View Answer

Given \(\rho = 4\text{ g/cm}^3\). New mass unit \(M' = 100\text{ g}\) and new length unit \(L' = 10\text{ cm}\). \(\rho = 4 \frac{1/100 M'}{(1/10 L')^3} = 4 \frac{1/100}{1/1000} \frac{M'}{L'^3} = 40 \frac{M'}{L'^3}\).

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Question 52: easy

If \(x = at + bt^2\), where \(x\) is the distance travelled by the body in kilometres while \(t\) is the time in seconds, then the units of \(b\) is:

[1989]

1. \(km/s\)
2. \(km s\)
3. \(km/s^2\)
4. \(km s^2\)
View Answer

By homogeneity, \([bt^2] = [x]\). So \([b] = [x]/[t^2] = km/s^2\).

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Question 53: easy

Plane angle and solid angle have:

[2022]

1. Both units and dimension
2. Units but no dimensions
3. Dimensions but no units
4. No units and no dimensions
View Answer

Plane angle (radian) and solid angle (steradian) are dimensionless quantities (ratios of lengths or areas) but possess units.

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Question 54: moderate

The dimension \([ML^{-2}T^{-2}A^2]\) belong to the:

[2022]

1. electric permittivity
2. magnetic flux
3. self inductance
4. magnetic permeability
View Answer

The dimension of magnetic permeability is \(MLT^{-2}A^{-2}\). The given dimension \(ML^{-2}T^{-2}A^2\) does not match a standard physical quantity listed. Assuming a typo and it refers to magnetic permeability.

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Question 55: moderate

If \(E\) and \(G\) respectively denote energy and gravitational constant, then \(\frac{E}{G}\) has the dimensions of:

[2021]

1. \([M][L]^{-1}[T]^{-1}\)
2. \([M^{2}][L]^{0}[T]^{0}\)
3. \([M^{2}][L]^{-2}[T]^{-1}\)
4. \([M^{2}][L]^{-1}[T]^{0}\)
View Answer

Energy \([E] = ML^2T^{-2}\) and Gravitational Constant \([G] = M^{-1}L^3T^{-2}\). So \([E/G] = M^2L^{-1}T^0\).

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Question 56: easy

Dimensions of stress are:

[2020]

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

Stress is Force per unit Area. \([\text{Stress}] = [F]/[A] = (MLT^{-2})/L^2 = ML^{-1}T^{-2}\).

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Question 57: easy

The dimensions of \((\mu_0\epsilon_0)^{-1/2}\) are:

[2012 Mains]

1. \([L^{1/2}T^{-1/2}]\)
2. \( L^{-1}T \)
3. \([LT^{-1}]\)
4. \([L^{1/2}T^{1/2}]\)
View Answer

The speed of light \(c = 1/\sqrt{\mu_0\epsilon_0}\). Therefore, \((\mu_0\epsilon_0)^{-1/2} = c\). The dimensions of speed are \([LT^{-1}]\).

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Question 58: easy

The dimension of \(\frac{1}{2}\epsilon_0 E^2\), where \(\epsilon_0\) is permittivity of free space and \(E\) is electric field, is:

[2010 Pre]

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

The expression \(\frac{1}{2}\epsilon_0 E^2\) represents electric energy density, which is Energy per unit Volume. \([\text{Energy density}] = [\text{Energy}]/[\text{Volume}] = (ML^2T^{-2})/L^3 = ML^{-1}T^{-2}\).

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Question 59: moderate

Which two of the following five physical parameters have the same dimensions?
A. Energy density
B. Refractive index
C. Dielectric constant
D. Young’s modulus
E. Magnetic field

[2008]

1. (A) and (D)
2. (B) and (D)
3. (C) and (E)
4. (A) and (D)
View Answer

Energy density (A) is \(ML^{-1}T^{-2}\). Young's modulus (D) is Stress/Strain, so also \(ML^{-1}T^{-2}\). Therefore, (A) and (D) have the same dimensions.

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Question 60: moderate

Dimensions of resistance in an electrical circuit, in terms of dimension of mass \(M\), of length \(L\), of time \(T\) and of current \(I\), would be:

[2007]

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

Resistance \(R = V/I = (W/q)/I = W/(I^2T)\). Work \([W] = ML^2T^{-2}\). So, \([R] = (ML^2T^{-2})/(I^2T) = ML^2T^{-3}I^{-2}\).

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