CIE AS & A Level Physics : 1.2 SI units – Exam style question – Paper 1

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Question

The drag coefficient \(C_{d}\) is a number with no units. It is used to compare the drag on different cars at different speeds. It is given by the equation

\(C_{d} = \frac{2F}{\rho v^{n}A}\)

where F is the drag force on the car, ρ is the density of the air, A is the cross-sectional area of the car and v is the speed of the car.

What is the value of n?

A    \(1\)                B     \(2\)            C    \(3\)            D     \(4\)

Answer/Explanation

Ans:     B

 

Since the drag coefficient is a constant, therefore it is unit less, hence the units of the numerator and denominator must be the same therefore

[ N ] = [(kg/m^3)(m/s)^n)m^2 ]
[ kg ms^{-2}] = [ kg (m/s)^n m]
[kg m s^{-2}] = [ kg m^{n-1}s^{-n}]
Solving for n we get,
n = 2
Hence the second option (B) is correct.
 

Question

One property Q of a material is used to describe the behaviour of sound waves in the material. Q is defined as the pressure P of the sound wave divided by the speed v of the wave and the surface area A of the material through which the wave travels:

\(Q = \frac{P}{vA}\).

What are the SI base units of Q?

A   \(kg\, m^{2}\, s^{–3}\)         B    \(kg\, m^{–3}\, s^{–1}\)          C     \(kg\, m^{–4}\, s^{–1}\)           D     \(kg\, m^{–2}\, s^{–2}\)

The unit of the quantity Q is given as,

[Q] = [\frac{F}{vA}]

[Q] = [\frac{(kg m/s^2)/m^2}{ (m/s)m^2}]

[Q] = [kg m^{-4}s^{-1}]

 

Answer/Explanation

Ans:    C 

Question

The Y-input terminals of a cathode-ray oscilloscope (c.r.o.) are connected to a supply of amplitude \(5.0\)V and frequency \(50\)Hz. The time-base is set at \(10\)ms per division and the Y-gain at \(5.0\) V per division.

Which trace is obtained?

The time period is given as,

T = 1/f

= 1/50 = 0.02 s

= 20 ms

In the graph A, the time period is 10 ms since the wave is repeating itself after 1 time base of 10 ms. Hence the option (A) is incorrect.

In the graph B, the time period is 20 ms and the amplitude of the voltage is less than 5 V, therefore the option (B) is incorrect.

In the graph C, the time period is 10 ms therefore the option (C) is incorrect.

 

Answer/Explanation

Ans:    D

Question:

What is the unit of weight in terms of SI base unit(s)?

 A \(kg~ms^{-1}\)          B \(kg~ms^{-2}\)          C \(n\)           D \(J~m^{-1}\)

Answer/Explanation

B

The weight is given as, 

W = mg

hence the unit is weight is

[W] = [kg ms^{-2}]

 

Question

  What is a possible unit for the product VI, where V is the potential difference across a resistor and I is the current through the same resistor?

A     newton per second \(N~s^-1\)
B     newton second \(N~s\)
C     newton metre \(N~m\)
D     newton metre per second \(N~m~s^-1\)

Answer/Explanation

Ans:D

We know that the power is given as,

P = VI

therefore the units of VI is that of power, also we know that the power is given as,

P = Fv

therefore the units of power can be given as,

[P ] = Newton meter per second Nms^{-1}

Hence the option (D) is correct.

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