UNIVERSITY OF SURREY
SCHOOL OF ELECTRONICS AND PHYSICAL SCIENCES
DEPARTMENT OF PHYSICS
BSc and MPhys Programmes in Physics
LEVEL HE1
PAPER y
Principles of Physics
Time allowed: ? hours
ANSWER ? QUESTIONS
Internal Examiner:
External Examiner:
Dr Stephen Sweeney
Professor Mark Smith
The only University approved calculators are Casio Models FX115MS,
FX115W or FX115S for September 1998 entry onwards.
The numbers at the end of each section of a question give an
approximate indication of the marks available.
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SECTION A: ANSWER ALL QUESTIONS
1.
If the radius of the Earth is R, and the acceleration due to gravity at the surface is g, what is the
acceleration due to gravity at a height


2  1 R above the Earths surface?
(a) 0.5g
(b) 2g
(c) g
(d)
(e)
2.
g


2 1 g
Prior to the metric system, the French unit of length was the toise, where 1 toise = 1949 mm.
The toise was divided into 6 Paris feet, each of which was divided into 12 pouces, that were
further subdivided into 12 lignes. How many cubic lignes occupy the same volume as 1 cubic
centimetre?
3.
(a)
8.71x10-2
(b)
0.871
(c)
8.71
(d)
87.1
(e)
871
Which of the following statements is true for any collision?
(a)
The total energy and momentum are conserved and the centre of mass velocity is
constant.
(b)
The total energy, kinetic energy and momentum are conserved and the centre of mass
velocity is constant.
(c)
The kinetic energy and momentum are conserved and the centre of mass velocity is
constant.
(d)
The total energy, kinetic energy and momentum are conserved and the centre of mass
velocity may vary.
(e)
The total energy and momentum are conserved and the centre of mass velocity may
vary.
4.
Calculate the determinant:
0 1 1
1 0 0
0 1 1
(a) -2
(b) -1
(c) 0
(d) 1
(e) 2
5.
A boulder of mass m slides with constant velocity down the side of a volcano at an angle 
with respect to the horizontal. Which one of the following expressions correctly relates the
magnitude of the frictional force, fk, to the coefficient of kinetic friction, k ?
(a) f k   k mg
(b) f k   k mg cos
(c) f k   k mg sin 
(d) f k  0
(e) The coefficient of kinetic friction is not appropriate for this problem.
6.
A fictitious planet called Nietsnie has a mass of 106 zix and a density of 10 zix/fiz3. If 1 fiz =
50 km, and assuming that Nietsnie is spherical, what is the radius of Nietsnie ?
(a) 3100 m
(b) 1.44 x 106 m
(c) 1440 m
(d) 5.8 x 10-4 m
(e) 3.10 x 106 m
7.
An electron makes a transition from a high energy state to a low energy state, releasing a
photon in the process. The wavelength, λ, of the photon is measured to be 1240nm. Given that
Ephoton=hc/λ, this is equivalent in energy to:
(a) 1.6 x 1016 J
(b) 1.6 x 10-16 J
(c) 1.6 x 1019 J
(d) 1.6 J
(e) 1.6 x 10-19 J
8.
The extension, d, of a spring which obeys Hooke's law is proportional to the tension, F, which
has produced it. Therefore, F=kd. The dimensions of the constant, k, in terms of mass [M],
length [L] and time, [T] are:
(a) [M][L]2[T]-2
(b) [M][T]-2
(c) k is a dimensionless constant
(d) [M]-1[T]2
(e) [L][T]-1
9.
What is the vector product a  b where a = ( iˆ + ĵ +2 k̂ ) and b = ( iˆ +2 ĵ + k̂ ) ?
(a) -3 iˆ - ĵ - k̂
(b) -3 iˆ - ĵ + k̂
(c) -3 iˆ + ĵ - k̂
(d) 0
(e) -3 iˆ + ĵ + k̂
10.
Two forces of ( iˆ + ĵ + k̂ ) N and (2 iˆ -2 ĵ - k̂ ) N act on an object. The unit vector in the direction
of the resultant force is:
(a) (3 iˆ - ĵ ) N
(b)
(c)
(d)
(e)
11.
10 N
1
10
1
2
(3 iˆ - ĵ ) N
(3 iˆ - ĵ ) N
1
10
(-3 iˆ + ĵ ) N
An object moves from iˆ m to ( iˆ + ĵ - k̂ ) m whilst being acted upon by a force ( iˆ + ĵ + k̂ ) N.
What is the work done by the force on the object?
(a) 0 J
(b) 2 J
(c) ( iˆ + ĵ ) J
(d) 1 J
(e)
12.
5 J
A particle moves in a circle with constant angular velocity, ω . If the origin of co-ordinates is
at the centre of the circle, which one of the following statements concerning the velocity, v ,
and position, r , of the object is false?
(a) r is constant
(b) r is constant
(c) v is constant
(d) v  ω  r
(e) v  r
13.
Which of the following is not an SI base unit?
(a) volt
(b) kelvin
(c) mol
(d) metre
(e) candela
14.
A car has an acceleration given by a = 2t iˆ -3t2 ĵ +5 k̂ ms-2. What is the velocity of the car as a
function of time given that at t = 2s, v = iˆ + ĵ + k̂ ms-1 ?
(a) (t2+3) iˆ +(t3-9) ĵ +(9-5t) k̂ ms-1
(b) (t2-3) iˆ +(9-t3) ĵ +(5t-9) k̂ ms-1
(c) -t3+t2+5t ms-1
(d) t2 iˆ -t3 ĵ +5t k̂ ms-1
(e) 2t iˆ -3t2 ĵ +5 k̂ ms-1
15.
Which of the following is a true statement for two bodies making an inelastic collision ?
(a) Only momentum is conserved.
(b) Kinetic energy and momentum are conserved.
(c) Neither total energy nor momentum are conserved.
(d) Total energy is not conserved.
(e) Total energy and momentum are conserved but kinetic energy is not.
30 marks
SECTION B: ANSWER TWO QUESTIONS
1.
(a)
Explain the “Principle of Superposition of Forces”. If a particle is acted upon by several forces
but maintains a constant velocity, state a relationship between the forces.
3 marks
(b)
A particle moves in a straight line from position 3 iˆ m to position (4 iˆ +2 ĵ ) m under the action
of a force given by x iˆ +z ĵ +y k̂ N. Calculate the work done by the force.
6 marks
(c)
A particle of charge q has a speed of 105 ms-1 and is travelling in the z = 0 plane at an angle of
45° to both the x and y axes.
(i)
Write down an expression for the velocity of the particle in terms of the unit vectors, iˆ
and ĵ .
The particle enters a region containing a uniform magnetic field B and a uniform electric field
E. The particle experiences a force due to the magnetic field equal to q(v  B) and a force due
to the electric field of qE.
(ii)
Assuming that the magnetic field is in the z direction and has a magnitude of 10T, write
down an expression for the force acting on the particle due to the magnetic field.
(iii)
Calculate the magnitude and direction of the electric field E required to ensure that the
particle moves within this region at constant velocity.
(iv)
In the absence of the electric field, with the aid of a diagram, describe the motion of the
particle in the magnetic field.
11 marks
2.
(a)
State whether the total energy, kinetic energy and momentum are conserved in:
(i)
(ii)
an elastic collision
an inelastic collision
Explain what is meant by a perfectly inelastic collision.
3 marks
(b)
Two particles, of mass, m1 = m kg and m2 = 2m kg, have velocities, v1 = ( iˆ - ĵ ) ms-1 and
v2 = (4 iˆ +2 ĵ ) ms-1, respectively.
(i)
Calculate the centre-of-mass velocity for this system.
(ii)
These two particles collide in a perfectly inelastic collision to produce a composite
object of mass 3m. What is the momentum of the composite object as viewed from the
centre-of-mass frame of reference?
(iii)
What is the final velocity of the composite object as viewed from the laboratory frame?
(iv)
What fraction of the total kinetic energy has been lost in the collision?
10 marks
(c)
Prove that, for a system containing an arbitrary number of particles, the total laboratory frame
kinetic energy is equal to the sum of the kinetic energies of each particle as viewed from the
centre-of-mass frame of reference and the kinetic energy of the total mass moving with the
centre-of-mass velocity.
7 marks
3.
(a)
Define angular velocity and moment of inertia. State their units of measurement. Explain
briefly the physical meaning of moment of inertia.
6 marks
(b)
The angular momentum L of an object at position r with respect to an origin O is,
L = r x p , where p is its linear momentum. Show that the rate of change of angular
momentum is equal to the applied torque.
4 marks
(c)
The moment of inertia of a disc of mass m and radius d spinning through its centre and
perpendicular to the plane of the disc is
1
md 2 . Hence or otherwise show that the moment
2
of inertia of a uniform sphere of radius a and mass M rotating about its centre is equal to
2
Ma 2 .
5
Assuming that the Earth is spherical with a radius of 6400 km and that it has a constant
density of 5500 kgm-3, calculate the moment of inertia of the Earth due to its spin.
10 marks