UNIVERSITIES OF** **MANCHESTER
LIVERPOOL

LEEDS SHEFFIELD AND BIRMINGHAM

**JOINT
MATRICULATION BOARD**

**________________________________**

GENERAL CERTIFICATE OF** **EDUCATION

**PHYSICS—Paper II**

ADVANCED

Tuesday 1 June 1965 9.30 - 12.30

**Careless and untidy work will be
penalized**.

*Answer ***nine** *questions including:*

(a) **six** *questions from *SECTION
(1):

(*b*)* ***three ***questions
from *SECTION (2).

*Candidates are advised to spend
about *15 *minutes
on each *SECTION** **(1) *answer and about 30 minutes on each *SECTION**
**(2) *answer.*

**Answers to Sections (1) and** **(2)** **must be written
in different answer-books.**

*The books must be marked clearly
either *SECTION**
**(1) *or *SECTION (2) *and handed in to the Supervisor separately.*

*Candidates should wherever
possible show by their answers that they have seen or themselves performed
experiments on the subjects they are discussing.*

*For full credit it is not
sufficient to obtain correct results to numerical questions; the principles involved
and their bearing on the question must be clearly stated.*

*Assume that the acceleration due
to gravity is*

*981
cm.sec. ^{2} and that one calorie is
equivalent to 4.2 joules.*

* Mathematical tables are supplied.*

**91 ADV. UU**** ***Turn over*

* *

2

SECTION
(1)

*Answer
***six ***questions from this section.*

**1. **Derive
an expression for the time period of vertical oscillations of small amplitude
of a mass suspended from the free end of a light helical spring.

What deformation of the wire of
the spring occurs when the mass moves?

**2**. Explain in terms of molecular forces why some
liquids spread over a solid surface whilst others do not.

A**
**glass capillary tube of uniform bore of diameter 0.050 cm. is held
vertically with its lower end in water. Calculate the capillary rise. Describe
and explain what happens if the tube is lowered so that 4.0 cm. protrudes above
the water surface. Assume that the surface tension of water is 70 dyne cm.^{-1}

**3. A **brass
wire of diameter 1.0 mm. and density

8.5 gm.cm.^{3 }is
stretched under a tension of 2.0 kgm.wt. between bridges 50 cm. apart.
Calculate its fundamental frequency when vibrating transversely.

A horse-shoe magnet** **is
placed so that the wire, at its centre, passes between the poles and a current
is passed along the wire. Draw a diagram to illustrate the directions of the
magnetic field, the current and the force on the wire. Describe what is
observed if an alternating current of constant amplitude is used and the
frequency of the current is slowly increased from 20 c.p.s. to 100 c.p.s.

**4.** Describe
the processes which lead to the formation of numerous dark lines (Fraunhofer
lines) in the solar spectrum. Explain why the positions of these lines in the
spectrum differ very slightly when the light is received from opposite ends of
an equatorial diameter of the sun.

92 ADV.

3

**5.*** *When light is incident in a
metal plate electrons are emitted only when the frequency of the light exceeds
a certain value: How has this been explained?

The
maximum kinetic energy of the electrons emitted from a metallic surface is 1.6
x 10^{-12}** **erg when the frequency of the incident radiation is
7.5 x* *l0^{14} c.p.s. Calculate the minimum frequency of
radiation for which electrons will be emitted.
Assume that Planck’s constant = 6.6 x 10^{-27} erg sec.

**6.** An isolated conducting spherical shell of
radius10 cm., in vacuo, carries a positive charge of 1.0 x l0^{-7}
coulomb. Calculate (*a*)* *the electric field intensity, (*b*)
the potential, at a point on the surface of the conductor. Sketch a graph to
show how one of these quantities varies with distance along a radius from the
centre to a point well outside the spherical shell. Point out the main features
of the graph.

(Candidates
using the c.g.s. system of units may assume that 1 coulomb = 3.0 x l0^{9}
e.s.u. of charge;

those using the rationalized M.K.S. system, that the
electric space constant = 8.85 x l0^{-12} farad m.^{-1}.)

**7.** Describe
in detail how. using a Wheatstone bridge arrangement, you wouId measure the
mean temperature coefficient of resistance between 0^{o} C . and 100°
C. for iron wire.

**8.** What is an *electron-volt *?** **Assuming
that the charge on an electron is 1.60 x 10^{-19} coulomb express one
electron-volt in terms of another unit

Calculate
the kinetic energy and velocity of protons after being accelerated from rest
through a potential difference of 2.00 x 10^{5} volt.

(Assume that the
mass of a proton = 1.67 x10^{-24} gm.)

92 ADV** ***Turn over*

4

SECTION
(2)

**(Answers
to be written in a separate answer-book.)**

*Answer
***three ***questions from this section.*

**9. **State Newton’s second law of
motion.

Show that a force must act on a
particle moving in a circle with constant speed, and derive an expression for
this force.

What is the nature of the force
maintaining the motion of (*a) *an artificial satellite, (*b*)* *an
electron in a hydrogen atom?

Observations are made of the
period of revolution and height of an artificial satellite revolving about the
earth in a circular orbit. Show how an estimate of the mass of the earth may be
made by using the observations and other necessary data.

**10. **Describe, with the aid of a
labelled diagram. how you would find the specific heat of a liquid by the
method of continuous flow.

Discuss the advantages and
disadvantages of the method compared with the method of mixtures.

The temperature of 50 gm. of a
liquid contained in a calorimeter is raised from 15.0^{o} C. (room
temperature) to 45.0° C. in 530 sec. by an electric heater dissipating 10.0
watts. When 100 gm. of liquid is used and the same change in temperature occurs
in the same time, the power of the heater is 16.1 watts. Calculate the specific
heat of the liquid.

**11. **Explain in detail how, with the
aid of a pin and a plane mirror, you would determine the focal length of a thin
bi-convex lens.

Having found the focal length of
this lens, explain how you would find the radius of curvature of one of its
faces by Boys' method. Discuss whether or not this method can be used to find
the radii of curvature of the faces of a thin converging meniscus lens.

The radii of curvature of the
faces of a thin converging meniscus lens of material of refractive index 3/2
are

5

10 cm. and 20 cm. What is the focal length of the lens
(a) in air, (*b*)* *when completely immersed in water of refractive
index 4/3?

**12.
**In an
experiment using a spectrometer in normal adjustment fitted with a plane
transmission grating and using monochromatic light of wavelength 5.89 x l0^{-5}
cm., diffraction maxima are obtained with telescope settings of 153° 44’, 124^{o}
5’, 76^{o} 55’ and 47° 16’, the central maximum being at 100^{o}
30’. Show that these observations are consistent with normal incidence and
calculate the number of rulings per cm. of the grating.

If this grating is replaced by
an opaque plate having a single vertical slit 2.00 x 10^{-2} cm. wide,
describe and explain the diffraction pattern which may now be observed.
Contrast the appearance of this pattern with that produced by the grating.

**13.** Define
*intensity of magneti:ation I *and *magnetic susceptibility k, *and
with the aid of a diagram explain what is meant by *hysteresis.*

Sketch a graph showing how *I *varies
with the applied magnetizing field as the field applied to a specimen of soft
iron, initially unmagnetized, is slowly increased from zero. On the same diagram
sketch the corresponding graph for steel.

By reference to your earlier
account state, with reasons, desirable magnetic properties of materials to be
used as (a) the core of an electromagnet, (*b*)* *the core of a
transformer, (*c*)* *a permanent magnet.

**14. **A given material is described as
being *radioactive *with a *half-value period (half-life) *of 2 days.
Explain the terms printed in italics.

Describe and explain experiments
that could be performed to identify the types of radiation which radioactive
substances can emit.

92 ADV.