Units and Measurements
Test 1

Correct answer Carries: 4.

Wrong Answer Carries: -1.

The dimensional formula of force is:

Force is given by \( F = ma \).

Mass has the dimension \([M]\) and acceleration has the dimension \([LT^{-2}]\).

So, the dimensional formula of force is \([MLT^{-2}]\).

[MLT⁻²]
[ML²T⁻²]
[M⁰LT²]
[MLT⁰]
1

Which of the following is not a base unit in the SI system?

SI system consists of 7 base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd).

Kelvin
Candela
Newton
Mole
3

The number of significant figures in 0.00450 is:

Leading zeros are not significant. The digits 4, 5, and the trailing zero are significant.

2
3
4
5
2

The SI unit of pressure is:

Pressure is force per unit area. \( P = \frac{F}{A} \).

Since force has units of Newton (N) and area has units of \(m^2\), the SI unit of pressure is Pascal (Pa) or \( N/m^2 \).

Newton
Pascal
Joule
Watt
2

The unit of Planck’s constant is:

Planck’s constant \( h \) appears in the equation \( E = h \nu \), where energy has units of Joule (J) and frequency has units of Hertz (Hz) or \( s^{-1} \).

Thus, \( h \) has the unit \( J \cdot s \) or \( kg \cdot m^2 \cdot s^{-1} \).

Joule-second
Newton-meter
Joule
Watt
1

The number of base units in the SI system is:

The SI system has 7 base units: metre, kilogram, second, ampere, kelvin, mole, and candela.

5
6
7
8
3

If the percentage error in measuring mass and velocity are 2% and 3% respectively, the maximum possible error in kinetic energy is:

Kinetic energy is given by \( KE = \frac{1}{2} m v^2 \).

Using error propagation: \( \frac{\Delta KE}{KE} = \frac{\Delta m}{m} + 2 \frac{\Delta v}{v} \).

Substituting the given values: \( 2\% + 2(3\%) = 8\% \).

5%
6%
7%
8%
4

Which of the following has the same dimensions as energy?

Energy has the unit \( Joule = kg \cdot m^2 \cdot s^{-2} \).

Work and torque also have the same dimensions.

Power
Force
Torque
Momentum
3

The dimensional formula of work is:

Work is given by \( W = F \cdot d \).

Since force has the dimensional formula \( [MLT^{-2}] \) and distance has \( [L] \), work has the dimensional formula \( [ML^2T^{-2}] \).

[MLT⁻²]
[ML²T⁻²]
[M⁰LT²]
[MLT⁰]
2

In a new unit system, \( 1 \, \text{unit of mass} = 0.25 \, \text{kg} \), \( 1 \, \text{unit of length} = 0.1 \, \text{m} \), \( 1 \, \text{unit of time} = 0.5 \, \text{s} \). What is \( 3 \, \text{J} \) (\( 1 \, \text{J} = 1 \, \text{kg m}^2 \text{s}^{-2} \)) in this system?

\( [J] = [\text{M L}^2 \text{T}^{-2}] \). \( 3 \, \text{J} = 3 \, \text{kg} \times (1 \, \text{m})^2 \times (1 \, \text{s})^{-2} = 3 \times (4 \times 0.25) \times (10 \times 0.1)^2 \times (2 \times 0.5)^{-2} = 3 \times 1 \times 1 \times 4 = 12 \, \text{new units} \).

9.0
12.0
15.0
18.0
2

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