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Multiple Choice Questions

Measurement, Physics 11

Choose the best possible answer;

  1. What is the radian measure between the arms of watch at 5:00 pm?
A. 1 radianB. 2 radian

C. 3 radian

D. 4 radian

Explanation: The whole watch is 2π radian. It is divided into 12 parts (each of 1 hr). Therefore, the radian measure between any two numbers is (2π/12 = 1/6 π = 0.167π rad). At 5:00 pm, one arm is at 12 and the other at 5. Therefore, the radian measure between the arms will be 0.167 π × 5 = 0.167 × 3.14 × 5 = 2.6 rad ≅ 3 rad.

2. 10 = ………….

A. 0.01745 radian B. 1 radian C.3.14 radian 2πradian

Solution: Degree measure of the whole circle = 3600

                   Radian measure of the whole circle = 2π

Equating, 3600 = 2π radian ⇒ 10 = (2π/360) radian ⇒ 10 = (2 × 3.14)/360 radian = 0.01745 radian

3. The metric prefix for 0.000001 is

A.      Hecto

B.      micro

C.      deka

D.      nano

Solution: 0.000001 = 1 × 10-6 and prefix for 10-6 = micro.

4. Which of the following is the correct way of writing unit?

A.      71 Newton

B.      12 mμs

C.      8 Kg

D.      43 kgm-3

Explanation: (A) Newton is the name of Sir Isaac Newton, the scientist. When we mean the unit of force, we write newton. So 71 newton is correct. (B) The repeated multiple is not correct. Instead of 12 mμs (this is 12 mili micro second), we should write 12 ns (nano second). (C) Name of the unit is considered to be a simple noun and should not start with capital letter. The correct way of writing is 8 kg.

5. A student measure the distance several time. The readings are between 49.8 cm and 50.2 cm. The measurement is best recorded as,

A.      (49.8 ± 0.2) cm

B.      (49.8 ± 0.4) cm

C.      (50.0 ± 0.2) cm

D.      (50.0 ± 0.4) cm

6. The percent uncertainty in the measurement of (3.76 ± 0.25) m is

A.      4%

B.      6.6%

C.      25%

376%

Solution: Uncertainty in 3.76 cm = 0.25 cm

                    Uncertainty in 1 cm      = 0.25/3.76 = 0.0664893617

                   Uncertainty in 100 cm   = 0.0664893617 × 100 = 6.64693617 = 6.6 cm

(Rounded off to two significant digits as 0.25 has the least number of sig figs which is 2).

7. The temperature of two bodies measured by a thermometer are t1 = (20 ± 0.5) °C and t2 = (50 ± 0.5) °C. The temperature difference and the error therein is

A.      (30 ± 0.0) °C

B.      (30 ± 0.5) °C

C.      (30 ± 1) °C

D.      (30 ± 1.5) °C

Explanation: Rule for finding uncertainty in subtraction (and also addition) is that the uncertainties in both measurements are added. Uncertainties in both measurements are 0.5 cm. Adding them gives 1 cm which is the uncertainty in the difference of both measurements.

8. (5.0 m ± 4.0%) × (3.0s ± 3.3%) =

A.      15.0 ms ± 13.2%

B.      15.0 ms ± 7.3%

C.      15.0 m ± 0.7%

D.      15.0 ms ± 15.3%

Explanation: Rule for finding uncertainty in multiplication (and also division) is that the percentage uncertainties in both measurements are added. So, add 4.0% and 3.3% in the final result.

9. (2.0 m ± 2.0%)3 =

A.      8.0 m3 ± 1.0%

B.      8.0 m3 ± 2.0%

C.      8.0 m3 ± 5.0%

D.      8.0 m3 ± 6.0%

Explanation: The power rule for finding uncertainty is that the percent uncertainty is multiplied with the power. Therefore, multiply 2.0% by 3 to get 6.0% and add it with the cube.

10. The number of significant figures in measurement of 0.00708600 are

A.      3

B.      4

C.      6

D.      9

Explanation: The rule is 0’s to the left are not significant. 0 between the significant digits are significant and all 0’s to the right are significant. Therefore, the first three 0’s are not significant. The remaining all digits (i-e, 708600) are significant which are 6.

11. How many significant figures does 1.362 + 25.2 have?

A.      2

B.      3

C.      5

D.      8

Explanation: Add the numbers. It gives 26.562. Use the sum rule and round off the answer to 1 decimal place. The answer is 26.6. Hence, there are 3 sig figs in the answer.

12. Compute the result to correct number of significant digits.

1.513 m + 27.3 m = ………

A. 29 m

B. 28.8 m

C. 28.81 m

D. 28.813 m

Explanation: To find the significant digits in addition, the rule is we round off the result to the least precise input number. This simply means, to the number which has least decimal places. The input numbers are 1.513 and 27.3. Now 27.3 has 1 decimal place (less than 1.513, which has 3 decimal places), therefore, the result should also have 1 decimal place. Therefore, option B is correct.

13. If 7.635 and 4.81 are significant numbers. Their multiplication in significant digits is

A.      36.72435

B.      36.724

C.      36.72

D.      36.7

Solution: 7.635 × 4.81 = 36.72435

Rule for rounding off is to retain as many significant digits in answer as there are in the numbers to be multiplied. Now, 7.635 has 4 sig figs and 4.81 has 3. Therefore, the answer should be rounded off to 3 sig figs which is option D.

14. The precision of the measurement 385000 km is

A.      10 km

B.      100 km

C.      1000 km

D.      1000000 km

Explanation: Precision depends upon the least possible value that can be measured. The least possible value that can be measured with an instrument is called least count. If we look at the given figure, 385000 km, we see the least count is 1000 km. (this means the next number on the scale would be 386000 km). Therefore, the correct option is C.

15. [M0L0T0] are dimensions of

Explanation: [M0L0T0] means no dimensions or dimensionless quantity.  All the above given quantities are ratios and dimensionless.

  • Strain is the ratio of change in length to the original length, ΔL/L. Dimensions in numerator and denominator are same and cancel each other.
  • Refractive index is the bending of light when it enters from one medium to another. It is equal to the ratios of velocities, for example, entering light from vacuum in a medium where its velocity is v. The refractive index is then c/v. Again dimensions above and below in the fraction are same and cancel each other.
  • Let we see something in microscope. The microscope magnifies (enlarges) it. The ratio of magnified size to the original size is called magnification. It is obtained by dividing the magnified size on the original size. Therefore, in numerator and denominator the dimensions are of size and cancel each other.

16. The dimensions of torque are

A.      [MLT]

B.      [M2L2T]

C.      [ML2T-2]

D.      [ML2T2]

Explanation: Torque is τ = rFsinθ

Dimensions of ‘r’ are [L], of F are [MLT-2] and sinθ is dimensionless. Put these values and get the answer.

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