# Jamb past questions and answers on vector and scalar quantities

#### (1) Answer True or False to the following questions

QUESTIONS

a. Both a spring balance and a chemical balance are used to measure the mass of an object.

False the spring balance is used to measure weight while the chemical balance is used to measure mass of an object.

b. Hooke’s law form the basis of operation of the spring balance

yes, because the more the spring balance stretch or extends determine the weight of an object. I.e the extension of a spring balance is proportional to the weight of the body.

C. The chemical balance works on the principle of moments.

True, because this involves two bodies and a lever.

d. A micrometer screw Guage can be used to measure the internal diameter of a tube.

False, because it’s used to measure the external diameter of an object and the internal diameter can be best done by a vernier caliper.

e. For a ruler graduated only in centimeters, measurement can be made accurately to the nearest millimeter.

False, because a measurement is limited to one-half of the smallest division on the ruler or 0.5cm (5 millimeter)

#### (2) Each of the quantities in the following list is indicated as a scalar or vector quantity. Answer True if the classification is correct and False of not.

QUESTIONS

a. Pressure [ vector]

b. Electrical potential [scalar]

c. Impulse [vector]

d. Heat capacity [scalar]

e. Altitude [ vector]

f. Electrical potential difference [vector]

g. Magnitude induction [scalar]

h. Acceleration due to gravity [vector]

i. Momentum [ vector]

j. Power [scalar]

k. Electrical field [scalar]

l. Electrical current [vector]

a. Pressure [ vector] True✓

b. Electrical potential [scalar] True✓

c. Impulse [vector] True✓

d. Heat capacity [scalar] True✓

e. Altitude [ vector] False ×

f. Electrical potential difference [vector] False ×

g. Magnitude induction [scalar] false×

h. Acceleration due to gravity [vector] True✓

i. Momentum [ vector] True✓

j. Power [scalar] True✓

k. Electrical field [scalar] False×

l. Electrical current [vector] false ×

#### (3) In the following list the unit of each quantity is indicated in brackets. Answer True(T) if the indicated unit is correct and False (F) if not.

QUESTIONS

a. Work [kgm²s-²]

b. Power [ Js]

c. Gravitational potential [jkg-¹]

d. Pressure [kgm-¹s-²]

e. Specific latent heat [ jkg-¹k-¹]

f. Density [ kgm-³]

g. Elastic modulus [Nm-¹]

h. Electric field [Nc-¹]

I. Potential difference [Jc-¹]

j. Resistivity [Ωm-¹]

a. Work kgm²s-²

##### Solution

Work = force × distance

= Mass × acceleration × distance

= Kg × ms-² × m

= Kgm²s-²

b. Power [ Js] [False]

##### Solution

Power = work done/ time taken

= (Force × distance)/time taken

= (Mass × acceleration × distance) time taken

= (Kg × ms-² × m)/s-¹ i.e j/s

= Kgm²s-³ or j/s

c. Gravitational potential [jkg-¹] True

d. Pressure [kgm-¹s-²] [ True]

##### Solution

Pressure = force/ area
= Mass × acceleration / area
= Kg × ms-² / m²
= Kg × ms-² × m-²
= Kgm-¹s-²
e. Specific latent heat [ jkg-¹k-¹]. (False)
solution
Specific latent heat is jkg-¹
f. Density [ kgm-³] True
g. Elastic modulus [Nm-¹] false
Solution
Nm-²
h. Electric field [Nc-¹]
True (Nc-1)
I. Potential difference Jc-¹
Voltage, V is the same as jc-¹
j. Resistivity Ωm-¹
Ωm

1. Which of the following are derived units?
I. Meter, II. coulomb, III. kilogram, IV. Ampere, V. Joule
A. I and III only.
B. II and V only.
C. II, IV and V only
D. All of them
First you’ve to know the meaning of derived units. Derived units consist of two or more fundamental units. So for instance, meter has only one fundamental units but coulomb and joule more than one fundamental unit.
For instance,
Joule = force× distance
= Mass × acceleration × distance
2. Which of the following are derived quantities?
I. Thrust II. Temperature III. Area. IV. Pressure
A. I and V only.
B. II, III and IV only.
C.. I, II and IV only
D. I, II, III and IV only
Thrust, area and pressure are derived units
Area = m² = i.e m×m (two fundamental units)
Pressure = force/area
So also thrust is a derive unit.
3. The derived dimension [ML²T-²] is a dimension of I. Acceleration. II. Torque. III. Energy
A. I only
B. III only
C. I and II only
D. II and III only
Sure by now, you should know it’s D
If you don’t still know, try to bring out the formula for energy
Energy = work done = force×distance
Mass × acceleration× distance
Mass = kilogram i.e M
Acceleration = ms-² i.e length × time-¹ = LT-²
Distance = meter = length, L
So therefore, = M×LT-²×L
ML²T-². ( So also for torque)
4. Which of the following are not fundamental units?
I. Kelvin II. Newton. III. Second. IV. Radian
5. The unit of momentum is
A. Js-¹. B.Ns. C. Ns-¹ D. Nms