LABORATORY MANUAL

PHY121

PHYSICS LABORATORY

List Of Experiments

Sr. No.

DESCRIPTION Page No.

0 An introduction to units, errors ,different types of graphs and measurement of length, mass and time

1 To study variation of angular acceleration with torque acting on the fly wheel. Find out the minimum torque required to overcome the friction between the flywheel and bearing and also find out the moment of inertia of the flywheel.

2 To study the dependence of force of friction on- 1. Normal Reaction 2. Area of contacts 3. Nature of Material 4. Nature of Surface

3 To plot graph between distance knife edges from the center of gravity and the time period of a compound pendulum.

4 To find the value of ‘g’ using simple pendulum.

5 To determine the value of acceleration due to gravity at a place by Kater's pendulum

6 To Find the moment of Inertia of an irregular body about an axis passing through its centre of gravity with a torsion pendulum.

7 To find out the energy band gap of a given semiconductor by using four probe method.

8 To determine the frequency of a electrically maintained tuning fork by using Melde’s experiment and hence verify the law of vibrating string

9 To determine the modulus of rigidity using Maxwell needle.

10 To study one dimensional elastic collision using two hanging sphere.

11 To Find the Young’s Modulus of the material of a rectangular bar by bending using traveling Microscope.

12 To find the unknown capacitance of a capacitor using flashing and quenching of neon bulb.

Experiment 0

Title: Simple measurements and graphical analysis

Equipment to used: Vernier callipers, screw gauge and multimeter

Material Required: Linear-linear and semi-log graph paper

Learning objective: (1) Students learn the use of Vernier caliper, screw gauge and multimeter

(ii) Students learn to plot linear-linear and semi-log graphs

Introduction: The precision of length measurements may be increased by using a device that

uses a sliding vernier scale. Two such instruments (identify in the picture above) that are based

on a vernier scale which you will use in the laboratory to measure lengths of objects are the

vernier callipers and the micrometer screw gauge. These instruments have a main scale (in

millimetres) and a sliding or rotating vernier scale.

A multimeter is an electronic measuring instrument that combines several measurement

functions in one unit. A typical multimeter may include features such as the ability to measure

(AC/DC) voltage & current, resistance and testing of a diode.

Zero error occurs when the measuring instrument registered a reading when there should be

none.

Least count of a measuring instrument is the smallest quantity that can be measured accurately

using that instrument. The degree of accuracy of a measurement can be concluded from the

least count of the instrument

Procedure:

Part A (Measurement)

1. To find the density of the given material

You are given a rectangular block and you have to find the density of material of which the

rectangular block is made of. We know density(d) =[mass(m kg)/volume (V m3)].

To find the volume of the rectangular block measure its length, width and height by vernierc

caliper.

Take at least five readings of each dimension. Also remember to check and note in your

“report sheet” the zero error and least count of the vernier caliper you are using. Even if

“zero error” is “zero” entry should be recorded in your report sheet.

Next measure the mass of the rectangular block using a balance; take at least five readings.

Also note “zero error” and “ least count” of the balance you use for finding the mass.

Tabulate the data, calculate the density along with the possible error.

Error in density(d)

d=m/V or d/d= (m/m)+ (V/V) (derive this expression)

Estimate (m) and (V) to estimate the error (d) in the density you have found out in your

experiment.

2. To find the resistivity of a given metal wire

You will need screw gauge and a multimeter for this experiment.

Resistivity (=

Resistance(R ohms) [ area of cross-section of the wire (A m2)/ length of the wire(l m)]

Derive the units of

Take a piece of a metal wire of almost uniform cross-section; measure (at leat five times) its

cross section by screw gauge and length (at least five times) by vernier caliper. Measure the

resistance of the above piece of wire using a multimeter( at leat five times)

Tabulate the data and calculate along with possible errors.

Error in

= R A/l so that RRAAll

How do you estimate A?

Part B (graphical analysis)

Linear graph paper

Let us consider the case of time period „T‟ of a simple pendulum which is written as

T = (2) (L/g)1/2

----------(1)

„L‟ is the “length” of the pendulum while „g‟ is acceleration due to gravity. Eq. (1) can be

rewritten as

T2 = (4

2/g) L---------(2)

Eq. (2) is an equation of straight line with slope = (42/g) and intercept = 0

One can find the value of “g” from the graph of T2 with L.

In one of the experiments on simple pendulum a student came up with the following data

Table 1

S. No Time for 10 oscillations

(s)

Effective length of the pendulum

(m)

1 16 0.6

2 18 0.8

3 20 1.0

4 22 1,2

5 24 1,4

6 25 1.6

7 27 1.8

8 28 2.0

Find the value of “g” by plotting the above data i.e T2 Vs L; T is the time period of the

pendulum for its effective length L.

How to plot the graph

Step 1. From Eq. 2 we have to plot T2 vs L (L should in meter)

Prepare the Table with following headings (prepare directly in your Lab Report Sheet)

Sample Table

S.No. L

(m)

T

(s)

T2

1. 0.6 1.6 2.56~2.6

Step 2. Choose a “linear” graph sheet which is linearly (normally in mm) graduated on both X

as well Y- axis

Step 3. Choose Y-axis for T2 and X-axis for L

Step 4. Max T2 is 1 and min is 0.25; choose your scale so that you can mark 0.25 clearly.

Similarly choose scale for L on X-axis.

Step 5. Mark the points on the graph with a sharp pencil

Step 6. Draw a straight line through the points so that maximum number of points are very

close to the line (Best fit we will not discuss presently)

Step 7. Find the slope from the graph and calculate “g”

Exercise

In the above experiment the error ( in time period T is (0.1s) while the length L has error

(L) equal to 0.01m. Calculate the error in “g”

Semi-log graph paper

Radioactive decay is given by N(t) = N(0) e-at , where N(t) are the observed counts at time t,

N(0) are the counts at time t = 0 (fixed arbitrarily) and a is the decay constant. Calculate N(0)

and a by graphical technique from the given data (Table 2)

N(t) = N(0) e-at

Or ln N(t) = ln N(0) - t (ln is log to the base e)

Or 2.3log N(t) = 2.3 log N (0) -t (change of log base to 10)

Or log N(t) = log N(0) - (/2.3) t……………….(3)

This is an equation of a straight line with y=log N(t), x- - (/2.3) t with log N(0) as intercept

and plot of log N(t) vs t will give values of “” . Since y is in log form and x is in linear form

the plot has to to prepared using “semi-log” graph paper whose y-axis is in log scale while x-

axis is in linear scale.

Table 2 summarizes the data collected from an experiment on radioactive decay. Plot the data

on semi-log paper and calculate “” and N(0) for this decay.

Exercise: Half-life “’ is defined as the time needed to have [N(t)/N(0)]= ½; derive an

expression for “”.

Calculate the value of “” for the radioactive process tabulated in Table 2.

Table 2

Time (days) Relative Activity

0.2 35.0

2.2 25.0

4.0 22.1

5.0 17.9

6.0 16.8

8.0 13.7

11.0 12.4

12.0 10.3

15.0 7.5

18.0 4.9

26.0 4.0

33.0 2.4

39.0 1.4

45.0 1.1

Important:

(i) Give a title to the graph; in present case it will be T2 Vs L for a simple pendulum.

(ii) Mark scales on the graph sheet; X-axis “10mm = so many m” and Y-axis “10mm= so

many seconds”

(iii) Mark X-axis and Y-axis with quantity (along with units) you are plotting

(iv)Calculate the slope and “g” on the graph sheet so that a graph is complete and one need

not to refer to the Lab Sheets.

Interpolation: From the graph you can find the L for T=0.44 (for example, within the

present data set)) even though there is no experimental data; this process is called

interpolation.

Extrapolation: One can extend the length of the line so that one can predict L for T =0.1s or

2.5s (outside the present data set); this is called extrapolation.

Experiment 1

Aim: To study variation of angular acceleration with torque acting on the fly wheel. Find out

the minimum torque required to overcome the friction between the flywheel and bearing and

also find out the moment of inertia of the flywheel Learning Objectives:

Rotational dynamics

Learn to Measure the angular acceleration „α‟, torque „τ‟ and hence moment of inertia of the flywheel.

Learn to apply the principle of conservation of energy to rotational dynamics.

Learn to aware of the limitations in an experiment and devise method to solve the problems.

Learn to handle error estimation using sum of percent errors.

Apparatus Used: A wall mounted flywheel, slotted mass with hanger (50gm each), a strong and

thin string or fine cord, stop watch, meter rule or measuring tape and vernier callipers.

Diagram and Theory:

Fig 1 Typical flywheel, slotted weights with hanger and thread

The Newton‟s law for linear motion that rate of change of linear momentum is equal to

applied force causing the change, F= dP/dt=d(mv)/dt=ma (m=mass and a is linear

acceleration) becomes for angular motion as:

Applied torque dL/dt= d(I)/dt= I where I the rotational equivalent of mass is called

“moment of inertia” and “” is angular acceleration. Note “”, “L” and “” are all vectors.

Note that = r x F where F is the force applied at a distance „ r‟ from the axis of rotation.

Exercise: Figure out differences between mass and moment of inertia

Fig 2 Experimental setup

A torque “‟ to a flywheel, in this experiment, is applied by a mass “M” falling under

gravity. This mass M is attached to one end of a thread while the other end is attached to the

axle of the flywheel. This resulting torque “”causes rotational motion in the flywheel.

However, the friction in the bearings of the flywheel results in the frictional torque “f” on the bearings which oppose the motion of the flywheel.

Procedure:

Examine the wheel and see that there is the least possible friction. Measure the diameter of the axle with vernier calipers at different points and find the mean.

Take a strong and thin string whose length is less than the height of the axle from the floor. Make a loop

at its one end and slip it on the pin A on the axle. Tie a suitable mass to the other end of the string.

Suspend the mass by means of the string so that the loop is just on the point of slipping from the pin A. Note the position of the lower surface of the mass „m‟ on a scale fixed behind on the wall.

Now rotate the wheel and wrap the string uniformly round the axle so that mass is slightly below the

rim of the wheel. Count the number of turns wound the axle and let it is „n‟. The wheel will thus make n revolutions before the thread detached.

With the help of stopwatch note the time taken by the mass to descend through a height „h‟

Repeat step-5 keeping m constant and varying the number of turns n. Take 6-7 readings.

Again repeat step-5 keeping the number of turns n constant and varying the mass m. Take atleast 6 observations with different values of m. Repeat each observation thrice and calculate the average time

taken in each observation.

Scope of the result expected:

The student will learn about torque, angular acceleration produced due to torque and hence

physical importance of the moment of inertia of circular bodies like wheels.

Parameter and Plots: Calculate Vernier constant of vernier calliper

Calculate the radius of the axle

To find angular acceleration:

Angular acceleration of the fly wheel can be calculated by calculating the time as given in step 5 and 6. Hence draw a graph between n and t2. Slope of this graph gives us the value of angular

acceleration.

To find out torque acting on the flywheel:

Suppose the mass m, when released, starts moving downward with acceleration α. Let T be the tension in the string. Then the torque acting on the string can be calculated by using these parameter.

To find out moment of inertia:

Plot a graph between angular acceleration along X-axis and torque along Y-axis. When we plot a graph between torque and angular acceleration, then slope of the straight line gives

the moment of the inertia. Also by using the values of torque and angular acceleration, moment of

inertia can be calculated.

Cautions:

Mass of string can be taken into account for better results.

Stop watch should be started and stopped with accuracy to avoid any kind of time interval

measurement error.

Experiment 2

Title: To measure the coefficient of friction between two surfaces using an inclined plane.

Equipment: Inclined plane with different surfaces, rectangular block, roller and weights

Learning objectives (i) Measurement of the coefficient of static sliding friction between two

surfaces using (i) weights and (ii) angle of repose concept

Outline of the procedure:

Fig 1 Typical inclined plane

Fig 2 Free body diagram of a mass resting on an inclined plane

At equilibrium (when block is at rest with respect to inclined plane)

m g sinf (force of friction)= s N (s is the coefficient of static friction)

m g cos m g sin)/s

Or s = tan ; can be adjusted so that the block is about to slide; this is called the angle of

“repose” which is characteristic of the surfaces in contact.

On other hand if a force “F” is applied parallel to the inclined plane such that the block is at the

verge of moving upwards than “F” is the measure of the static frictional force between the two

surfaces.

F(applied)= s N = s m g cos or s = F(applied)/m g cos

(1) Coefficient of static friction using a rectangular block and weights

Checks that the pulley fitted to the inclined plane is moving freely, if not lubricate it with

lubricating oil available in the LAB.

Attach one end of the thread to the scale pan and other end to the hook of the wooden block.

Place the block on the inclined plane and pass the thread over the pulley.

Place the weight on the pan and tap the surface of the inclined plane gently. If the block does

not move up go on adding weight to the pan till the block just begin to slide upwards on

tapping the surface gently.

Note down the (i)weight placed in the pan + weight of the pan and (ii) angle of the inclined

plane in your Lab report sheet/notebook.

Repeat it for two more angles of the inclined plane.

Repeat the above experiment for two more different surfaces of the inclined plane. Tabulate

the data

(2) Coefficient of static friction using a steel roller and weights

Repeat step (1) for a steel roller (use steel roller instead of wooden block), tabulate the data.

(3) Coefficient of static friction by finding angle of repose for a rectangular block

Detach the thread from the hook of the wooden block and let it be in equilibrium on inclined

plane. Find out “” when the block just begins to slide down. Note this angle to find s .

Repeat it with two more different surfaces of the inclined plane keeping same . Tabulate the

data

(4) Coefficient of static friction by finding angle of repose for a steel roller

Repeat step (3) for a roller.

(5) Compare the values of the s obtained by two different approaches. Explain the

discrepancy. Also calculate the error in s.

Precautions

(i) All the surfaces should be dry and dust free

(ii) Adjust the thread so that it is parallel to the inclined plane

(iii) Pan should not touching any part of the inclined plane

Experiment 4

Experiment Title: To find the acceleration due to gravity by using simple pendulum.

Equipments to be used: A stand, a bob, thread and stopwatch

Learning Objectives:

To find the length of pendulum by using the concept of centre of mass.

To understand small angle swinging.

Procedure:

1. Find the length of simple pendulum when it is at rest vertically.

2. Tilt the bob to a small angle and note down the time period of 10 oscillations by using

stopwatch.

3. Repeat the observation 5 times.

4. Find out the time period of one complete oscillation and calculate the value of g.

Parameters:

If the amplitude of oscillation is small, the time period t of simple pendulum is given by

g

lt 2

Where l = length of the pendulum

g = acceleration due to gravity

Scope of the Result:

Simple pendulum is the simplest technique to find the value of acceleration due to gravity at

any place on the surface of earth.

Cautions:

1. The length of the pendulum should be measured from the centre of the bob.

2. Use cotton thread which is supposed to be inextensible and weightless.

3. The amplitude of oscillation should be small.

4. The fan should be switched off to avoid external forces.

5. The pendulum should be firmly hanged with the help of a leveled stand.

Experiment 7

Title: To find the energy band gap of the semiconductor material by using the four probe

method.

Learning objective:

To find the band gap of semiconductor.

To study the variation of resistivity with temperature.

Equipment To Be Used: Probes arrangement, sample crystal (Germanium), oven, four probes

setup with digital voltmeter (range 0 to 200mV and 0 to 2V) and constant current generator

(range is 0 to 20mA)

Outline of procedure:

Put the sample on the base plate of the four probe arrangement. Unscrew the pipe holding the

four probes and let the four probes rest in the middle of the sample. Apply a very general

pressure on the probes and tighten the pipe in this position. Check the continuity between the

probes for proper electrical contents.

Place the four probe arrangement in the oven and fixed the thermometer in the oven through

the hole provided.

Switch on the Ac main of four probe set up put the digital meter in the current measuring mode

through the selector switch. In this LED facing mA would glow. Adjust the current to a desire

value(say 5 mA)

Note down the readings of milli voltmeter with the rise in temperature and corresponding value

of temperature.

Plot the graph between 1/T along x-axis and ln ρ along y-axis. (T is absolute temp)

Scope of the results expected:

Slope = lnρ1 – lnρ2 / 1/ T1- 1/T2.

Band gap (EG) = 2K * slope of the graph between 1/ T and lnρ

Band gap (EG) …………………….Electron volt

Parameter:

Voltage with rise in temperature

Resistivity and conductivity.

Plots:

Plot between 1/T and lnρ

Caution:

The Ge crystal is very brittle. Therefore apply minimum pressure for proper electrical contacts.

Connect the outer pair of probes leads to the constant current power supply and the inner pair

of probes to the voltage terminals.

The resistivity of the material is uniform in the area of measurement.

Measurement should be made on surface which has high recombination, such as mechanical

lapped surfaces.

The surface on which the probe rest is flat with no surface leakage.

The four probes used for resistivity measurement contact the surface at points that lie in a

straight line.

The boundary between the current carrying electrodes and the bulk material is hemispherical

and small in diameter.

Experiment No. 9

Aim: To determine the modulus of rigidity of copper wire by Maxwel’s needle.

Equipments to be Used: A Maxwell‟s needle, a copper wire of suitable length & thickness, a

fixed support with tension head, a telescope with a scale attached to its stand , stop watch, a

screw gauge, a spring balance, a meter rod & an electric lamp with holder.

Experiment 12

Title: To find the unknown capacitance of a capacitor using flashing and quenching of neon

bulb. Equipment Required: A condenser of unknown capacity, 3 condensers of known Capacity (say 32μF,

50 μF, and 100 μF), resistance of the order of few mega-ohm, a Neon flashing bulb, stabilized DC

power supply of 250V; one way keys.

Learning Objectives: Here we find the capacitance using quenching and flashing of neon. A neon lamp consists of a small glass bulb filled with neon gas at low pressure with two electrodes.

When the electrodes connected to a D.C source stray electrons in the gas are attracted towards the

positive electrode. As voltage is increased, the speed of electrons also increases and at particular

voltage speed becomes high to ionize the gas so lamp begins to conduct and glows. This voltage is

known as flashing potential. When we place a capacitor in parallel with lamp, due to conduction of

lamp capacitor begins to discharge through it. It continues to do this until quenching potential reached

when neon lamp ceases to conduct. The capacitor then begins to charge again and whole process goes

on repeatedly. The flashing and quenching time can be determined by noting time taken by lamp for „n‟

consecutive flashes and quenches.

If t1 is time taken by capacitor voltage to fall from V1 to V2 and t2 is time for voltage to rise from V2 to

V1, then V2 = V1 e(- t

1/RC)

or t1 = -CR loge V2/V1 And

V2 = V1 (1- e(- t

2/RC)

) or t1 = -CR loge (1 - V2/V1)

T = t1 + t2 = C [-R loge V2/V1- R loge (1 - V2/V1)]

As R, V1 and V2 have constant fixed values, so we get T= k C where k is constant.

Circuit diagram:

Outline of the Procedure:

Draw the diagram and make the connections as in the fig.

Connect the condenser C1 in the circuit by inserting K1. Also insert the key K to connect power supply and increase the voltage till neon lamp just begins to flash. As already explained, the bulb starts

flashing and quenching as it is connected in parallel with the condenser. Note the flashing and

quenching time for 20 flashes. Take out the key K so that the power supply is disconnected.

Put in the key K4 for the circuit of unknown capacity C0.Since C1 and C0 are in parallel their capacities get added up and total capacity in parallel with the lamp is (C1 + C0). Again insert the key K

and adjust the power supply voltage to previous value. Note the time for 20 flashes. Remove the key K1

and K4. Now repeat the experiment with the capacity C2, C3 and with all the three known capacitor connected

together in parallel with Co.

Scope of result expected: By Connecting the condensers of known capacity in parallel with

lamp and with unknown condenser, time t for 20 flashes with and without unknown

capacitance can be obtained.

Parameters and Plots: Quenching and Flashing Time without unknown capacitor: t0

Quenching and Flashing Time with unknown capacitor: t1

Plot two graphs between values of capacitance along x-axis and flashing and quenching time t (without

and with unknown capacitance) y-axis For three different values of flashing and quenching time draw

three straight lines parallel to x-axis cutting the two graphs at A and B, C and D, E and F respectively

The unknown capacitance Co = AB = CB - CA

= CD = CD - CC

= EF = CF - CE Mean Co= ………μF

Cautions: Count the number of flashes very carefully.

Connections should be tight.

Capacitors should always be connected parallel to the lamp.

The voltage from D.C power supply should remain constant throughout the experiment.