Select the correct question of the following questions.

(i) Which of the following quantities has not expressed in proper units?

(a) stress/strain = newton/meter | (b) surface tension = newton/meter | (c) Energy= kg m/s |
(d) pressure = newton/meter^2 |

**Solution: **Unit of energy

Comparison proves the Energy is not expressed in proper units.

(ii) Which of the following correctly represent the S.I unit of pressure?

(a) Newton meter^{-2} (b) Newton^{2} m^{-1}

(c) Pascal ☛** (d) newton meter ^{-2}**

**Solution:** Pressure = Force/Area = newton meter^{-2}.

**Note:** The unit of force is newton, named after Sir Issac Newton. When we mean Sir Newton, we write Newton. When we mean unit of force, we write newton.

(iii) Which of the following may be used as valid formula to calculate speed of ocean waves? v= speed, g = acceleration due to gravity, λ = wave length, ρ= density, h = depth

**Solution: **The assertion can be proved by the dimensional consistency of the equation. Dimensionally written,

[LT^{-1}] = [L LT^{-2}]^{1/2} → [LT^{-1}] = [L^{2}T^{-2}]^{1/2} → [LT^{-1}] =[LT^{-1}]

This proves the dimensional consistency of the first option.

(iv) What is the S.I unit of the constant k in the following equation?

F = 6πηrv = krv

Where F = force, v = velocity and r = radius.

☛** (a) kg m ^{-1} s^{-1}** (b) kg m s

(c) kg^{-1} m^{2}s (d) kg m^{2} s^{2}

Solution

(v) Which of the following is the smallest value.

(Can you solve the remaining questions? Do it and compare the results)

Note: E = Exa = 10^{18}

(a) 10^{-6}m ☛** (b) μ** (c) 10^{6} (d) 10μ

**Solution**

(Note: Ratio of two similar quantities is dimensionless).

(vii) In a cricket match 500 spectators were counted one by one. How many significant figures will be there in the final result?

☛** (a) 3** (b) 1 (c) 2 (d) 0

(viii) The equation relating pressure and density is p =ρgh. How can both sides of this equation be written in terms of base units?

(a) [N m^{-1}] =[kgm^{-3}][ms^{-1}][m] (b)[Nm^{-2}] = [kgm^{-3}][ms^{-2}][m]

☛ **(c)[kgm ^{-1}s^{-2}] = [kgm^{-3}][ms^{-2}][m]** (d) [kgm

^{-1}]=[ms

^{-2}][m]

**Solution:** Since pressure is defined as force per unit area, therefore,

Changing into dimensional form, we have

(ix) A series of measurements of the acceleration of the free fall ‘g’ is shown in the table which set of results is precise but not accurate.

A | 9.81 | 9.79 | 9.84 | 9.83 | 9.79 |

B | 9.81 | 10.12 | 9.89 | 8.94 | 9.42 |

C | 9.45 | 9.21 | 8.99 | 8.76 | 8.51 |

☛D |
8.45 | 8.46 | 8.50 | 8.41 | 8.47 |

**Solution:** Observing all the 4 sets of data, we see the measurements in set D are close to one another but relatively far away from the actual value, 9.8. See question 4.

(x) A mass m has acceleration a, it moves through a distance s in time t. The power used in accelerating the mass is equal to the product of force and velocity. The percentage uncertainties are; 0.1% in m, 1% in a, 1.5% in s and 0.5% in t. What is the percentage uncertainty in average power?

(a) 2.1% (b) 2.6% ☛** (c) 3.1% ** (d) 4.1%

**Solution:** Since

Percentage uncertainty in mass = 0.1

Percentage uncertainty in acceleration = 1

Therefore, percentage uncertainty in product

Percent uncertainty in S = 1.5

Percent uncertainty in t = 0.5

Therefore percentage uncertainty in

Similarly, percentage uncertainty in the product

See question 4, product rule for further details.

(xi) Which one is a pair of the SI base units?

(a) ampere, joule (b) coulomb, second ☛** (c) kilogram, Kelvin** (d) meter, newton

Remember, joule, coulomb and newton are not base units.

(xii) What is the ratio 1μm/1Gm

(a) 10^{-3} (b) 10^{-9} (c) 10^{-12} ☛** (d) 10 ^{-15}**

Solution:

(xiii) A student measured the diameter of a wire using a screw gauge with least count 0.001 cm. The correct measurement is

(a) 5.3 cm (b) 5.32 cm ☛** (c) 5.320 cm** (d) 5.3200 cm

Since the least count is 0.001, the first two measurements are not precise enough and the last one has one digit guessed.

(xiv) The dimensions of frequency f are …..

(a) [T^{-2}] (b) [LT^{-1}] ☛** (c) [T ^{-1}] ** (d) [MT

^{-1}]

(xv) Which one is the least sub multiple.

(a) pico (b) femto ☛** (c) atto ** (d) neon

Hint: See table of prefixes, question 2.

(xvi) One femto is equal to;

(a) 10^{15} ☛** (b) 10 ^{-15}** (c) 10

^{-16}(d) 10

^{-9}

Hint: See table of prefixes.

(xvii) The scientific notation of a number 0.0023 is expressed as…

2.3×10^{-3}