CIE AS & A Level Physics : 1.2 SI units - Exam style question

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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

$[2F] = [\rho v^n A ]$

$[ N ] = [(kg/m^3)(m/s)^n)m^2 ]$

$[ kg ms^{-2}] = [ kg (m/s)^n m]$

$[kg m s^{-2}] = [ kg m^{n-1}s^{-n}]$

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

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.

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

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