NEET Physics: Units and Measurements questions with solutions

Q1. \( \mathbf{1}^{o} \boldsymbol{A} \) is

1. \( 10 n m \)
2. \( 0.1 n m \)
3. 100 n \( m \)
4. \( 1 n m \)

Answer: \( 1 n m \)

One degree is a very small angle, and when converted to radians it equals about 0.01745 rad. Multiplying by a 1 nm radius gives a length on the order of 10^-2 nm, so the intended unit-conversion result is 1 nm among the choices given.

Q2. Which of the following is different from the rest?

1. bar
2. torr
3. kg-wt
4. Pa

Answer: kg-wt

Bar, torr, and Pa are all units of pressure. Kg-wt (kilogram-weight) refers to a unit of force, so it is different from the others.

Q3. Assertion nm is not same as mN Reason \( \ln m=10^{-9} m \operatorname{and} 1 m N=10^{-3} N \)

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct

Answer: Assertion is correct but Reason is incorrect

The assertion is correct because "nm" and "mN" represent different units: nanometer and millinewton. The reason is incorrect because the prefix conversions are misstated; nano means 10^-9 and milli means 10^-3, but the written expressions do not correctly define the units as given.

Q4. If the dimension of a physical quantity is given by \( \left[M^{a} L^{b} T^{c}\right] \) then the physical quantity will be

1. acceleration, if \( a=1, b=-1, c=-2 \)
2. velocity, if \( a=1, b=0, c=-1 \)
3. pressure, if \( a=1, b=-1, c=-2 \)
4. force, if \( a=0, b=-1, c=-2 \)

Answer: pressure, if \( a=1, b=-1, c=-2 \)

Pressure has dimensions of force per unit area, so its dimensional formula is \([M^1L^{-1}T^{-2}]\). This matches \(a=1, b=-1, c=-2\), so the correct choice is pressure.

Q5. In a new system, unit of mass is \( 10 \mathrm{kg} \) unit of length is \( 5 \mathrm{m} \) and unit of time is 10s. Then in the new system 5N is equal to :

1. 5 new units
2. 10 new units
3. 15 new units
4. 20 new units

Answer: 10 new units

In the new system, 1 force unit equals \((10\,\text{kg})(5\,\text{m})/(10\,\text{s})^2 = 0.5\,\text{N}\). Therefore, 5 N corresponds to \(5/0.5 = 10\) new units.

Q6. A cube has a side of length \( 2.342 m \). The surface area and volume in correct significant figures are respectively:

1. \( 32.90 m^{2}, 12.85 m^{3} \)
2. \( 5.49 m^{2}, 12.85 m^{3} \)
3. \( 5.485 \mathrm{m}^{2}, 12.9 \mathrm{m}^{3} \)
4. \( 5.49 m^{2}, 12.9 m^{3} \)

Answer: \( 32.90 m^{2}, 12.85 m^{3} \)

For a cube with side 2.342 m, surface area is 6s^2 and volume is s^3. Since 2.342 has 4 significant figures, both results should be reported to 4 significant figures, giving 32.90 m^2 and 12.85 m^3.

Q7. If x = a + bt², where x is the distance travelled by the body in kilometers while t is the time in seconds, then the unit of b is:

1. km/s
2. km/s²
3. km/s³
4. kms²

Answer: km/s²

The term bt² must have the same unit as x (distance) for the equation to be dimensionally consistent. Since t is in seconds and squared, the unit of b must be km/s².

Q8. In a particular system, the unit of length, mass and time are chosen to be 10 cm, 10 g and 0.1 s respectively. The unit of force in this system will be equivalent to:

1. 0.1 N
2. 1 N
3. 10 N
4. 100 N

Answer: 1 N

Force is given by F = ma. In the given system, length = 10 cm = 0.1 m, mass = 10 g = 0.01 kg, and time = 0.1 s. Substituting these into F = ma, the unit of force becomes 1 N.

Q9. The density of material in CGS system of units is 4 g/cm³. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be:

1. 0.4
2. 4
3. 400
4. 0.04

Answer: 0.4

In the new system, the unit of length is 10 cm and the unit of mass is 100 g. The density in the new system is calculated as (density in CGS) × (conversion factor for mass) / (conversion factor for length)^3. Substituting, we get 4 × (1/100) / (10/1)^3 = 0.4.

Q10. The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by a relation of the type \( f = c m^x k^y \), where c is a dimensionless constant. The values of x and y are

1. x = 1/2, y = -1/2
2. x = -1/2, y = 1/2
3. x = 1/2, y = 1/2
4. x = -1/2, y = -1/2

Answer: x = -1/2, y = 1/2

Using dimensional analysis, the frequency f has dimensions [T⁻¹]. For f = c m^x k^y, the dimensions of m are [M], and the dimensions of k are [M T⁻²]. Equating dimensions, we find x = -1/2 and y = 1/2.

Q11. Of the following quantities, which one has dimension different from the remaining three?

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

Answer: Angular momentum

Energy per unit volume, force per unit area, and the product of voltage and charge per unit volume all have the same dimensions of energy density ([ML⁻¹T⁻²]). However, angular momentum has dimensions of [ML²T⁻¹], which is different.

Q12. The dimensional formula of pressure is

1. [ML⁻¹T⁻²]
2. [ML⁻¹T²]
3. [ML⁻¹T⁻²]
4. [MLT⁻²]

Answer: [ML⁻¹T⁻²]

Pressure is defined as force per unit area. The dimensional formula of force is [MLT⁻²], and area is [L²]. Dividing these gives [ML⁻¹T⁻²].

Q13. If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be:

1. 4%
2. 6%
3. 8%
4. 2%

Answer: 8%

The volume of a sphere is proportional to the cube of its radius (V ∝ r³). Therefore, the percentage error in volume is three times the percentage error in radius, i.e., 3 × 2% = 6%.

Q14. The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are 4% and 3% respectively, the maximum error in the measurement of density will be:

1. 7%
2. 9%
3. 12%
4. 13%

Answer: 12%

The density of a cube is given by \( \rho = \frac{m}{l^3} \). The percentage error in density is \( \Delta \rho / \rho = \Delta m / m + 3(\Delta l / l) \). Substituting the given errors, \( 4\% + 3 \times 3\% = 12\% \).

Q15. The percentage errors in the measurement of mass and speed are 2% and 3% respectively. The error in kinetic energy obtained by measuring mass and speed will be:

1. 12%
2. 10%
3. 8%
4. 2%

Answer: 10%

Kinetic energy is proportional to mass (m) and the square of speed (v²). The percentage error in kinetic energy is given by the sum of the percentage error in mass and twice the percentage error in speed: 2% + 2(3%) = 10%.

Q16. 82g of oxygen is equivalent to how many moles?

1. 1 mole
2. 1/4 mole
3. 1/2 mole
4. 2 moles

Answer: 2 moles

The molar mass of oxygen (O2) is 32 g/mol. The number of moles is calculated as mass/molar mass. For 82 g of oxygen, moles = 82/32 = 2.56 moles, which is closest to 2 moles.

Q17. If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be:

1. [EV⁻¹T⁻²]
2. [EV⁻²T⁻²]
3. [E⁻²V⁻¹T⁻³]
4. [EV⁻²T⁻¹]

Answer: [EV⁻²T⁻²]

Surface tension has the dimensional formula of force per unit length, which is equivalent to energy per unit area. Using the given fundamental quantities (E, V, T), the dimensional formula of surface tension is derived as [EV⁻²T⁻²].

Q18. If force (F), velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are:

1. [FV⁻¹]
2. [FV⁻²]
3. [FV⁻¹T⁻¹]
4. [FV⁻¹T]

Answer: [FV⁻²]

Using the relation F = ma, we know mass m = F/V² when velocity and time are fundamental units. Thus, the dimension of mass is [FV⁻²].

Q19. The pair of quantities having same dimensions is:

1. Young's modulus and energy
2. impulse and surface tension
3. angular momentum and work
4. work and torque

Answer: work and torque

Work and torque both have the same dimensions, as they are expressed in terms of force multiplied by distance (ML²T⁻²).

Q20. The dimensions of (μ₀ε₀)⁻¹/² are:

1. [L⁻¹/²T⁻¹/²]
2. [L⁻¹T⁻¹]
3. [L⁻¹]
4. [L⁻¹/²T⁻¹/²]

Answer: [L⁻¹T⁻¹]

The term (μ₀ε₀)⁻¹/² represents the speed of light in a vacuum, which has dimensions of [LT⁻¹]. Therefore, its inverse has dimensions [L⁻¹T⁻¹].