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Units

Practice Questions:

Question 1: easy

Using rules of significant figures what is the value of \(22.8\text{ m} \times 3.4\text{ m}\):

1. 77.52 \(\text{m}^2\)

2. 77.5 \(\text{m}^2\)

3. 78 \(\text{m}^2\)

4. 78.0 \(\text{m}^2\)

View Answer

The multiplication result must be rounded to the least number of significant figures among the measured values. Since 3.4 has only 2 significant figures, the result \(77.52\text{ m}^2\) is rounded to 2 significant figures, which is \(78\text{ m}^2\).

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Question 2: easy

Convert \(25\text{ dyne}\) to a system where fundamental units of mass, length & time are \(100\text{ g}\), \(100\text{ cm}\) and \(1\text{ hour}\):

1. 43200

2. 34200

3. 3240

4. 32400

View Answer

Using \(n_2 = n_1 [M_1/M_2]^1 [L_1/L_2]^1 [T_1/T_2]^{-2}\), we get \(n_2 = 25 \left(\frac{1}{100}\right) \left(\frac{1}{100}\right) \left(\frac{1}{3600}\right)^{-2} = 32400\).

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Question 3: easy

Assertion (A): Mass, length and time may be taken as fundamental quantities.

Reason (R): Mass, length and time are independent of one another.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

View Answer

Mass, length, and time are chosen as fundamental quantities because they are independent of each other and cannot be defined in terms of one another.

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Question 4: easy

Assertion (A): eV and joule are the S.I. units of energy used in modern physics and mechanics respectively.

Reason (R): Different types of energies require different units in S.I. units.

1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)

2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

3. (A) is true but (R) is false

4. Both (A) and (R) are false

View Answer

The SI unit of all forms of energy is the joule. Electron-volt (eV) is not an SI unit, and different forms of energy do not require different SI units.

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Question 5: moderate

The angle \(1’\) (minute of arc) in radian is nearly equal to,

[2020- Covid]

1. \(4.85 \times 10^{-4}\text{ rad}\)

2. \(4.80 \times 10^{-6}\text{ rad}\)

3. \(1.75 \times 10^{-2}\text{ rad}\)

4. \(2.91 \times 10^{-4}\text{ rad}\)

View Answer

Convert \(1'\) to degrees, then to radians. \(1' = (1/60)^\circ = (1/60) \times (\pi/180)\text{ rad} \approx 2.91 \times 10^{-4}\text{ rad}\)

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Question 6: moderate

The unit of thermal conductivity is

[2019]

1. \(W m^{-1} K^{-1}\)

2. \(J m K^{-1}\)

3. \(J m^{-1} K^{-1}\)

4. \(W m K^{-1}\)

View Answer

Thermal conductivity \(k\) relates heat flux to temperature gradient. So, \(k\) has units of \(W/(m \cdot K) = W m^{-1} K^{-1}\).

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Question 7: moderate

The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are:

[2012 pre]

1. \(kg m s^{-1}\)

2. \(kg/ms\)

3. \(kg s^{-1}\)

4. \(kg s\)

View Answer

Damping force \(F_d = -bv\). The constant \(b\) has dimensions \([F_d]/[v] = (MLT^{-2})/(LT^{-1}) = MT^{-1}\), which is \(kg s^{-1}\).

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Question 8: 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 9: 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 10: easy