Free Measurements MCQs with Answers

51. Which experimental technique reduces the systematic error of the quantity being investigated?

• A. Adjusting am ammeter to remove its zero error before measuring a current.
• B. Measuring several inter modal distance on a standing wave to find the mean inter modal distance
• C. Measuring the diameter of a wire repeatedly and calculating the average.
• D. Timing a large number of oscillation to find a period

Explanation: Systematic error is an error having a non-zero mean, so that its effect is not reduced when observations are averaged. Zero error is an example of systematic error. it cannot be reduced by taking the average rather it is reduced by changing the instrument or changing the procedure.A zero error is a systematic error. So adjusting an ammeter to remove its zero error before measuring a current.

52. A metal sphere of radius r is dropped into a tank of water. As it sink at speed v, it experience a drag force F given by F= krv, where k is a constant. What are the SI base units of k?

• A. kg m2s-1
• B. kg m2s-2
• C. kg m-1s-1
• D. kg ms-2

Explanation: The following is the solution:F=krv which is equal to F/rvk=F/rv=kgms-2/m.ms-1=kgm-1s-1.

53. Which of the following is a dimensionless quantity?

• A. Power
• B. Frequency
• C. Refractive Index
• D. Impulse

Explanation: Refractive index of a medium is the ratio of the speed of light in a vacuum to the speed of light in that particular medium. Since the speed of light in vacuum and the speed of light in different mediums have the same dimensions, a quantity which is the ratio of these two will be dimensionless. Therefore, option C is the correct answer.For power, the formula is Energy/time and its dimensions are ML2T-3 .For frequency, the formula is 1/time period and its dimension is T-1.For impulse, the formula is force x time and its dimensions are MLT-1 . So amongst all four, only refractive index is the one having no dimensions.

54. If the units of length and force are increased four times, then the unit of energy will:

• A. Increase 8 times
• B. Increase 16 times
• C. Decrease 16 times
• D. Increase 4 times

Explanation: E=mc2 c=s/t Hence dimensionally, E=ML2T-2 E=(MLT-2)(L) =(4)(MLT-2)(4)(L)=16(ML2T-2)

55. If velocity, force and time are taken to be fundamental quantities, then the dimensional formula for mass will be:

• A. KV-1FT-1
• B. KV-1FT
• C. KVF-1T-1
• D. KV-1F-1T

Explanation: The following is the solution: F=Ma a=V/T M=FT/V

56. A rectangular plate has length (2±0.02) cm and width (1±0.01) cm. The maximum percentage error in the measurement of its area is:

• A. 1%
• B. 2%
• C. 3%
• D. 5%

Explanation: The following is the solution: % uncertainty of length= 0.02/2 x 100= 1% % uncertainty of width=0.01/1 x 100= 1% % uncertainty of the area of rectangle=1+1 =2%

57. In a resonance tube with a tuning fork of frequency 512 Hz, the first resonance occurs at water level equal to 30.3 cm, and the second resonance occurs at 63.7cm. The maximum possible error in the speed is:

• A. 51.2 cm/sec
• B. 102.4 cm/sec
• C. 204.8 cm/sec
• D. 153.6 cm/sec

Explanation: The following is the solution: Calculation of the error in the speed through inputting the given information in the formula Δv=2n(Δl2-Δl1), where Δv is the uncertainty of speed, n is the frequency, and (Δl2-Δl1) represents the uncertainty in the difference of the second and first resonance.

58. The dimensions of h/e (h = Planck's constant and e = electronic charge) are same as that of:

• A. Magnetic flux
• B. Electric flux
• C. Electric field
• D. Magnetic field

Explanation: The following is the solution: Plancks constant (h) has the units joule-seconds. the dimensions are =[ML2T−1], Electron charge (e) will have dimensions= [TI], Dimension for h/e will be [ML2T−2I−1], From the given options, Dimension for the electric field will be [M1L1I-1T-3], Dimension for magnetic flux will be [ML2T−2I−1], Dimension for electric flux will be [ML3T−3I−1], Dimension for the magnetic field will be [M1T-2I-1], Both magnetic flux and h/e will have the same dimensions.

59. The dimensions of σb4 (σ =Stefan's constant and b = Wein's constant) are:

• A. [M0L0T0]
• B. [ML4T-3]
• C. [ML-2T]
• D. [ML6T-3]

Explanation: The following is the solution: b=λmT, where λm is the peak wavelength of the black body radiation and T is the surface temperature of the black body.

60. Kilowatt hour is the unit of:

• A. Energy
• B. Electric charge
• C. Force
• D. Electric power

Explanation: The kilowatt-hour (SI symbol: kW⋅h or kW h; commonly written as kWh) is a unit of energy equal to 3600 kilojoules (3.6 megajoules). The kilowatt-hour is commonly used as a billing unit for energy delivered to consumers by electric utilities.