Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

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2730 questions · page 129 of 137 · choose a topic above to narrow them down

SA-PX-PI-0022 marksL2 StandardCalculatorAntimatter

An electron and a positron at rest annihilate into two photons. Calculate the frequency of each photon, in units of

10^{20}

Hz. (

0.511

MeV

=8.19\times10^{-14}

h=6.63\times10^{-34}

J s)

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SA-PX-PI-0041 markL2 StandardCalculatorConservation laws

In β⁻ decay,

n\to p+e^-+X

. Particle

X

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SA-PX-PI-0051 markL2 StandardCalculatorConservation laws

Which reaction is forbidden because baryon number is not conserved?

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SA-PX-RF-0022 marksL2 StandardCalculatorSnell’s law

Light passes from air into glass (

n=1.50

) at

40^\circ

to the normal. Calculate the angle of refraction in degrees.

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SA-PX-RF-0042 marksL2 StandardCalculatorOptical fibres

An optical fibre has core refractive index

1.48

and cladding refractive index

1.46

. Calculate the critical angle at the core–cladding boundary in degrees.

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SA-PX-RO-0042 marksL2 StandardCalculatorAngular momentum

A skater spins at

3.0

rad s⁻¹ with

I=4.0

kg m², then pulls her arms in so

I=2.0

kg m². Calculate her new angular velocity.

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SA-PX-RO-0052 marksL2 StandardCalculatorTorque

An engine delivers a torque of

50

N m at

600

revolutions per minute. Calculate the power in W.

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SA-PX-SG-0032 marksL2 StandardCalculatorSampling

CD audio is sampled at

44.1

kHz with

16

bits per sample on

2

channels. Calculate the bit rate in Mbit s⁻¹.

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SA-PX-SG-0042 marksL2 StandardCalculatorLC filters

Calculate the resonant frequency, in kHz, of an LC circuit with

L=10

mH and

C=100

nF.

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SA-PX-SR-0022 marksL2 StandardCalculatorDilation

Muons have a proper mean lifetime of

2.2

μs. Calculate the mean lifetime, in μs, measured on Earth for muons moving at

0.80c

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SA-PX-SR-0031 markL2 StandardCalculatorDilation

A spaceship of proper length

100

m passes Earth at

0.80c

. Calculate its length as measured from Earth, in m.

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SA-PX-SR-0052 marksL2 StandardCalculatorMass–energy

An electron (rest energy

0.511

MeV) moves at

0.60c

. Calculate its total energy in MeV.

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SA-PX-ST-0052 marksL2 StandardCalculatorDistances

A star has apparent magnitude

6.0

and is

100

pc away. Calculate its absolute magnitude.

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SA-PX-TE-0032 marksL2 StandardCalculatorResolution

Calculate the minimum angular separation, in μrad, that a telescope of aperture

0.10

m can resolve at a wavelength of

550

nm.

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SA-PX-TE-0052 marksL2 StandardCalculatorDetectors

The Lovell radio telescope has a

76

m dish and observes hydrogen emission at

0.21

m. Calculate its minimum resolvable angle in mrad.

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SA-ST-CS-0022 marksL2 StandardNon-calculatorContingency

In a contingency table with

N=100

, a cell's row total is 40 and column total is 50. Find its expected frequency.

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SA-ST-CS-0042 marksL2 StandardNon-calculatorGoodness of fit

Data in 7 classes (after combining) are tested for fit to a Poisson distribution whose mean is estimated from the data. Find

\nu

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SA-ST-CS-G012 marksL2 StandardCalculatorStatistic

A die is rolled 60 times giving

8,12,9,11,6,14

. Find

X^2

for a test of fairness.

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SA-ST-EX-0022 marksL2 StandardCalculatorMean and memory

Find the median of

\text{Exp}(3)

(3 s.f.).

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SA-ST-EX-0032 marksL2 StandardCalculatorProbabilities

X\sim\text{Exp}(0.5)

. Find

P(1<X<3)

(3 s.f.).

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