Activity-1

Aim-

To make a paper scale of given least count, e.g. 0.2 cm, 0.5 cm.

Apparatus –

A thick white paper sheet, pencil, scale with sharp edge marked in cm and mm, fevicol, a pair of scissors, a paper cutter, thick ivory sheet used by engineering students.

Theory –

As has been explained earlier least count of an instrument is the minimum reading which can be taken by using such instrument.

Range of the physical quantity to be measured is usually indicate on the top of the scale. Range is shown in the centre of the dial of instruments if graduations are marked in circle, as in current or voltage measuring instruments.

Procedure-

(A) Paper scale of least count 0.2 cm

1. Fold a white paper sheet in the middle along lengthwise.
2. Mark in the upper half along the length a line PQ 15 cm long by a sharp pencil (Fig. A).
3. Take P as zero mark points on PQ at a distance of 1.0 cm and write as 0,1, 2,……up to 15.

A: Scale of least count 0.2 cm.

B: Scale of least count 0.5 cm

1. Mark the vertical lines to line PQ at the position of each mark 0, 1, 2, up to 15.
2. Draw another sharp line RS which is parallel to PQ at a distance of 8 mm.
3. Draw another line XY parallel to PQ at a distance of about 25 mm. And complete the rectangle ABXY.
4. Now divide each 1.0 cm interval into five equal divisions on PQ by marking points at every interval of 2 mm. Mark these points up to 15 cm mark.
5. Now draw sharp small lines about 3 mm long perpendicular to PQ on each of the point which is separated by 2 mm.
6. Draw another line AB parallel to PQ at a gap of 3 mm.
7. Darken each line and division by the sharp black pen, and write 1,2,……15 at each cm mark.
8. Cut the rectangular scale by a sharp paper cutter and paste it on a thick ivory sheet and cut the sheet along the boundary of the rectangle with the help of scissors.
9. Paper scale of least count 0.2 mm and of the range of 15 cm is ready.

(B) Paper scale of least count 0.5 cm

1. Repeat steps 1 to 6 as in part A of the above activity.
2. Divide each 1.0 cm interval into two equal divisions on PQ by marking points at every interval of 5 mm and mark these points up to 15 cm mark (Fig. B).
3. Draw sharp small lines about 3 mm long perpendicular to PQ on each of the point which is separated by 5 mm.
4. Draw another line AB parallel to PQ at a gap of 3 mm.
5. Darken each line and division by the sharp black pen and write 1,2,…….15 at each cm mark.
6. Repeat the step 11 as in part A of the Activity 1.
7. Paper scale of least count 0.5 cm and of the range of 15 cm is ready.

(C) Measure the length of pencil with the paper scale

1. Place one end A of the pencil along the scale (A) in such a way so that A lies at full mark say 1 cm and read the position of the other end. Repeat the observation by placing the one end A of the pencil at 2 cm mark and take the reading of the other end.
2. Use the second scale (B) of least count 0.5 cm in the similar manner as explained in step 1 and record the observations.

Observation-

Least count of the scale (A) = ……..0.2 cm.
Table for length of the pencil using scale (A)

S.N.	Reading at one end A of the pencil a1 (cm)	Reading at other end B a2 (cm)	Length of the pencil = (a2 – a1) cm
1	1.0
2	2.0

Mean length of the pencil =………..cm.
Table for length of the pencil using scale (B)

S.N.	Reading at one end A of the pencil a1 (cm)	Reading at other end B a2 (cm)	Length of the pencil = (a2 – a1) cm
1	1.0
2	2.0

Mean length of the pencil =………cm.

Result-

1. The scales of the least count 0.2 cm and 0.5 cm have been made.
2. The length of the pencil, using scale (A) = …….cm.
   The length of the pencil, using scale (B) = ……….cm.

Precautions –

1. The cm markings should be longer than 0.2 cm and 0.5 cm markings.
2. Final lines and marking should be drawn by using fine tipped black ink pen.
3. Paper scale should be pasted on the thick ivory paper.
4. Use very sharp pencil for the graduation marks.

Sources of Error-

1. Graduation marks may not be equally separated.
2. The lines showing graduations may not be sharp as required.

Activity – 2

Aim –

To study the variation in the range of a jet of water with the angle of projection.

Apparatus –

A water pipe with a nozzle, a source of water under pressure (i.e. A tap connected to a tank or water supple line). A measure taps 5m long, a ply board protractor with radius of about 25cm and marked from 0^o to 180^o at an interval of 15⁰ each.

Making a protractor-

Take a circular ply board or ply sheet of radius about 25cm. Draw a long line through its centre as its diameter. Cut it in two halves to form dees. Draw the angles at an interval of 15⁰. Starting with 0⁰ and ending at 180⁰ on one of the dees. Fix it vertically on a wooden board.

Theory –

A jet of water possesses a projectile motion with the horizontal range R given as

R = (u₀² sin 2θ)/g, where θ is the angle of projection and u_o, velocity of projection.

Procedure-

• 1. Connect end of the water pipe to the water tap and fix a (metallic) jet at the other end.
  2. Turn on the tap and ensure that there is no leakage of water from the pipe. If it is there, make the connections water tight.
  3. Keep the protractor dee fixed vertically in front of you with its graduated on the right hand side.
  4. Place the jet at the center O of the projector and direct the nozzle of the jet along 15⁰ line on the dees.
  5. Open the tap to the maximum possible extent. The water coming out of the jet would fall on the ground at some distance from the centre of dees as shown in Fig. A-1. Ask your friend to mark on the ground, the point where the jet of water strikes the ground. Let this point be denoted as A. Close the tap.
  6. Change the angle of projection by fixing the nozzle of the jet along 30⁰ line.
  7. Repeat the step 5.
  8. Again ask your friend to mark on the ground, the point where the jet of water strikes the ground and label
  9. In this manner repeat the above step 6 for three more angle of projection, viz, 45⁰, 60⁰ and 75⁰, with the ground and mark the points where the jet of water strikes the ground as C, D and E respectively.
  10. Mark the position of the center of dees as O.
  11. Measure the distances OA, OB, OC, OD & OE with a measuring tap. These distances are representing the range R of water jet for variopus angles of projection taken.

Observation-

Least count of the measuring tape = ……………cm (say 5cm)

Table measurement of Range of Projectile

S.No.	Angle of projection of jet of water θ (in degrees)	Range of the water jet projectile R in (m)
1	15
2	30
3	45
4	60
5	75

Result-

Variation in the range of jet of water with the angle of projection is depicted in graph and it agrees with theory.

Precautions –

• 1. To obtain a jet of water with constant velocity, pressure head of water should be maintained constant.
  2. The position where the jet strikes the ground may not be a sharp point. Average distance at which the jet strikes should be measured for a given angle of projection.
  3. At least five observations at different angles of projection should be taken.

Sources of error-

1. The pressure of water may not remain constant.
2. The jet of water may not strike the ground at a sharp point but in a small area, therefore, its centre should be considered for measurement of the range.

 

Activity – 3

Aim – To measure the force of limiting friction for rolling of a horizontal plane.

Apparatus –

An inclined plane apparatus fitted with a glass top and a pulley, a small roller cart, weighing pan, weight box, spirit level spring balance and thread.

Theory-

According to principal of the connected motion tension in a string connected between a stationary object and a freely suspended weight, passing over a pulley in between same at both the ends.

To carry cut thin activity a roller cart placed on a horizontal flat plane is pulled as shown in figure. The pull is gradually increased till the cart is on the verge of motion. The force of limiting friction can be estimated. The force which opposes the motion of the block called force of rolling friction.

= μ₁ (constant) μ_1, is coefficient of rolling friction and N is the normal reaction.

Procedure –

• 1. Find the least count of the scale of the spring balance or table balance whatever is available.
  2. Note the zero error in the balance. Adjust the pointer to zero, if provision is there.
  3. Weight the block using table after finding its least count and zero error and record the weight as W.
  4. Set the plane surface horizontal by using a spirit level.
  5. Place the block with roller beneath it on the horizontal (Figure)
  6. Weight the pan in the balance and record it as W.
  7. Attach the pan to the hook of the block by a strong thread passing over the pulley so that you can apply a horizontal force on the block and can measure it too.
  8. Gradually add weights in the pan till the roller block system just starts rolling. Reduce the weights in the pan to minimum value for the roller to just start. Note the weights in the pan.

Record it as Q. Then (W + Q) g wt would be the limiting rolling frictional force (f_m).

• 1. Add 100 g wt on the block and repeat the above observation. Keep on adding 100 g wt on the block and repeat f_mr measurement. Do this three times more.
  2. Record your observation in a tabulated form as follows.

Observations –

Spring balance

Least count of the spring balance = …………….g wt

Zero error of spring balance = (e) = ……………..g wt

Zero correction = (-e) =……………….g wt

Weights of the wooden block

Observed weight = Wʾ = ……… g wt

Currected weight, W = Wʾ + (-e) = ………….. g wt

Weight of the pan = …………… g wt

Observed weight wʾ = ……………. g wt

Corrected weight , w = wʾ + (-e) = ……………… g wt

No. of observation	Weight on the block (g wt)	Weight of Block + wt. on it i.e. W+P = N (g wt)	Weight in the pan Q (g wt)	Weight of pan + wt. in it, i.e., w +Q =fmr (g wt)	Limiting force of rolling friction fmr (g wt)	Ratio Fmr/N
1
2
3
4
5

Result –

The mean value of μ_r = ……………….

Precautions and Sources of error –

1. The roller should have minimum friction. Check that they run freely.
2. The surface should be horizontal and smooth.
3. Force applied be pan balance and weight in it should be suitably adjusted.
4. The pan used should be light and fractional.
5. The system should be clean and dust free.

Activity – 4

Aim –

To observe change of state and plot a cooling curve for molten wax.

Apparatus-

Paraffin wax, beaker of 200 ml capacity, heating arrangement to melt the wax, thermometer clamp stand and a stop watch.

Theory-

The time rate of cooling of a hot body can be studied in terms of rate of fail of

It’s temperature i.e. where θ is the temperature and t is time.

When temperature difference between that of a hot body and that of its surrounding i.e.

(θ – θ₀) is small one can expect the newton’s law of cooling being obeyed. In that

case = -k (θ – θ₀) given a linear relationship between log of temperature (θ – θ₀) and time t. Thus our should expect a straight line in the graph when log of temperature difference (θ – θ₀) is plotted against time t.

Further, if there is a change in state e.g. a molten wax getting solidified, the latent heat also comes into picture. Due to this feature, it is expected that the temperature should becomes constant over time, as the wax gets solidified and cools down to the room temperature.

Diagram-

Procedure-

1. Set the tripod stand, heating arrangement, beaker and hard glass test tube with thermometer inserted through the cork tightly fitting into the mouth of the tube.
2. Bulb of the thermometer is lowered such that it is fully surrounded by wax.
3. Arrange the tripod, wire gauze, beaker and the burner as shown in figure B-1.
4. Clamp the test tube in a stand and adjust the height of the hard glass test tube such that ¾ of its part dips in water in the beaker.
5. Adjust the thermometer and turn it in such a way that graduation marks on it face towards you and you can see the level of mercury in the thermometer capillary and conveniently read the temperature.
6. The test tube surrounded by water in the beaker forms water bath for gradually heating the wax in the glass tube.
7. Turn the knob at the bottom of the burner such that right proportion of gas and air get mixed and ignite the gas. The water in the beaker starts heating.
8. As the temperature of water in the beaker rises, the contents of the test tube also show rise in temperature.
9. Record readings of temperature with the passage of time at 2 minute intervals. After attaining a certain value, the temperature stops rising and wax in the tube starts melting, i.e. changing its state from solid to liquid.
10. The temperature of wax in the glass tube remains steady (called melting point of wax till whole of wax melts. It starts rising when the heat is supplied continuously.
11. After the temperature rises about 20⁰C above the melting point, the heating is discontinued, the contents in the glass tube starts cooling.
12. Record temperature of gradually cooling wax inside the tube after intervals of every 2 minutes.
13. At a certain temperature, wax in seen to be solidifying. This temperature is called solidification point of wax. Continue recordings of temperature versus time.
14. Plot a graph of temperature versus time.
15. The graph you get is called the cooling curve. The curve depicts a certain part parallel to time axis. This porting shows the change of state from the liquid to solid.

Observation-

Least count of the scale of thermometer = ………….. ⁰C

Range of graduations of Celsius thermometer = …………………⁰C to …………⁰C

No. of Observation	Time ……….. (minutes)	Temperature of wax (0C)
1
2
3
4
5
6
7
8
9
10

Cooling curve-

Plot a graph between falling temperature of molten wax versus time taking temperature as ordinate and time along x-axis as abscissa.

Conclusion –

1. The temperature falls quickly in the beginning and then slowly.
2. When wax starts freezing the temperature does not fall further. The constant temperature is called freezing point of molten wax. From graph the freezing point of molten wax = …………..⁰C

Precaution-

1. Wax is an inflammable material, it should be handed with care, do not attempt to boil it.
2. If required the molten wax can also be periodically stirred as well.
3. Small wax pellets should be taken in the hard glass test tube.
4. The bulb of thermometer should be fully surrounded by wax.
5. The reading of temperature of wax, during the process of heating and cooling, should be recoded after intervals of every two minute.

Activity 5

Aim 
To study the effect of load on depression of a suitably clamped metre scale loaded at (i) its end (ii) in the middle.

Apparatus
A uniform straight wooden metre rod (scale). Two G clamp, pointer pin, thread, slotted weights of 50 g each, wax, vertical scale, clamp stand.

Theory 

Diagram 

Procedure 
(i) When metre scale is loaded at its end :
1. Clamp the metre scale firmly with G clamp at its one edge on the corner of table such that metre scale remains straight in horizontal plane.
2. The pointer pin or needle should be attached at free end of metre scale with wax.

3. Fix the scale on a stand vertically to take the reading.

4. Note the initial reading on vertical scale corresponding to the tip of the pointer when no weights is suspended.
5. Suspend the weights in steps at free end of metre scale with the help of a strong thread and note the corresponding readings on the vertical scale.

6. After taking 5-6 reading, start unloading the weights one by one and again note the reading on scale.
(ii) When metre scale is loaded in the middle :
7. Locate the C.G. of metre scale by suspending it with a thread.
8. Now, place the metre scale symmetrically on two knife edges them about 85 cm apart and check that metre scale is perfectly horizontal.
9. A pointer is attached at the mid point of the scale with the help of wax or adhesive tape to take the reading.
10. Repeat the steps 3 to 6 and record the observation in the table.

Observations 
1. Initial reading of pointer on vertical scale without loading at free end = x₀ =……..cm
Table for load and depression when metre rod is loaded at its one end.

S.No.	Load M (g)	Reading of free end of cantilever			Depression
		Loading	Unloading	Mean
1	50
2	100
3	150
4	200