Class 10 Physics Pba Notes and Solved Model Paper (FBISE)

A. Major experiments (Section A, 6 marks each)

P-Major 1. Radius and length of a metallic cylinder with vernier callipers

Apparatus: vernier callipers, metallic cylinder.
Least count (LC) = value of 1 main scale division / number of vernier divisions = 1 mm / 10 = 0.1 mm = 0.01 cm.
Reading = main scale reading (MSR, just before the vernier zero) + vernier coincidence number x LC. Correct for zero error: true reading = observed reading minus zero error.
Procedure: check zero error with jaws closed. Grip the cylinder between the jaws for length, then for diameter at three different places and in two perpendicular directions. Take the mean. Radius r = d/2.
Significant figures: an answer cannot have more significant figures than the least precise measurement, so round the final result (volume = pi r² l) to the same number of significant figures as the data.
Precautions: do not squeeze the object, read at eye level (avoid parallax), correct the zero error.

P-Major 2. Thickness of a wire with vernier callipers and a screw gauge

Screw gauge LC = pitch / number of circular scale divisions = 1 mm / 100 = 0.01 mm (0.001 cm). Pitch is the distance the screw moves in one full turn.
Reading = sleeve (linear) scale reading + circular scale reading x LC. Correct for zero error (positive if zero line is below the datum line, negative if above).
Precision: screw gauge (0.01 mm) is more precise than vernier callipers (0.1 mm), so use the screw gauge for thin wire.
Procedure: measure the diameter at 3 places along the wire and in 2 perpendicular directions each, take the mean. Use the ratchet to tighten, so the pressure is always the same.

P-Major 3. Motion of a ball rolling down an angle iron (distance-time graph)

Apparatus: angle iron (V-shaped channel), steel ball, stop watch, metre rule, wooden block or stand to raise one end, chalk or marker.
Procedure: incline the angle iron. Mark distances 200, 180, 160, 140, 120, 100 cm from the bottom. Release the ball from the top mark each time and time it to the bottom. Repeat for each distance, take t₁ and t₂, find the mean time t. Velocity = distance / mean time.
Graph: plot distance (y) against time (x). Constant velocity gives a straight line through the origin whose slope is the speed. A ball that speeds up gives a curve bending upward.
Effect of angle: a smaller angle of inclination means smaller acceleration, so the speed of the ball is less and the time taken is more.
Precautions: release without pushing, start and stop the watch together with the ball, keep the track clean and straight.

P-Major 4. Time period of a simple pendulum, relation between length and time period

Apparatus: cork or clamp stand, thread, metal bob, stop watch, metre rule.
Procedure: measure length L from the point of suspension to the centre of the bob. Displace the bob through a small angle (less than 10 degrees), release, time 20 oscillations, T = total time / 20. Repeat for 5 or more lengths (for example 40, 60, 80, 100 cm).
Relation: T = 2 pi sqrt(L/g). T² is directly proportional to L, so the graph of T² against L is a straight line through the origin. g = 4 pi² L / T² (about 9.8 m/s²). Period does not depend on the mass of the bob.
Why many oscillations: timing 20 oscillations reduces the reaction-time error.

P-Major 5. Specific heat capacity by the method of mixtures

Apparatus: calorimeter with stirrer, thermometer, metal (lead) shots, beaker, heater, balance, thread.
Procedure: find mass of the empty calorimeter m_c. Add water, find mass of water m_w, note its temperature T₂. Heat the metal in boiling water to T₁ (about 100 C), drop it quickly in the calorimeter, stir, note the highest temperature T.
Principle: heat lost by hot metal = heat gained by water and calorimeter.
m_s c_s (T₁ - T) = (m_w c_w + m_c c_c)(T - T₂), with c_w = 4200 J/kg K. Solve for c_s. Lead is about 130 J/kg K.
Precautions: transfer the metal quickly without splashing, insulate or lag the calorimeter, stir before reading.

P-Major 6. Temperature-time graph for ice and water, latent heats

Heating ice graph: rises from below 0 C, flat at 0 C (melting, latent heat of fusion), rises as water, flat at 100 C (boiling, latent heat of vaporization). On the flat parts the heat goes into breaking bonds (potential energy), not raising temperature.
Latent heat of fusion by mixtures: drop dry ice cubes at 0 C into warm water in a calorimeter. Heat lost by water and calorimeter = m_i L_f + m_i c_w (T - 0). Accepted value L_f = 334 kJ/kg (3.34 x 10⁵ J/kg).
Latent heat of vaporization: pass steam at 100 C into cold water, steam condenses and gives m_s L_v + m_s c_w (100 - T) to the water and calorimeter. Accepted L_v = 2260 kJ/kg.
Precautions: dry the ice with blotting paper, use a steam trap so no hot water enters.

P-Major 7. Image formed by a convex lens at different object positions

Object position	Image position	Nature and size
Beyond 2F	Between F and 2F	Real, inverted, diminished
At 2F	At 2F	Real, inverted, same size
Between F and 2F	Beyond 2F	Real, inverted, magnified
At F	At infinity	Very large, no image on screen
Between F and lens	Same side as object	Virtual, erect, magnified

Apparatus: optical bench, convex lens, lens holder, illuminated object (candle or cross-wire), white screen, metre scale.
Procedure: find focal length first by focusing a distant object on the screen (distance lens to screen = f). Then place the object at each position, move the screen to get a sharp image, record u and v. Lens formula: 1/f = 1/v + 1/u (real-is-positive convention). Magnification m = v/u.

P-Major 8. Resistors in series and parallel

Series: R_e = R₁ + R₂ (+ R₃). Same current through every resistor, total voltage V = V₁ + V₂. Adding another resistor increases the equivalent resistance and decreases the current.
Parallel: 1/R_e = 1/R₁ + 1/R₂. Same voltage across each, total current I = I₁ + I₂. R_e is smaller than the smallest resistor.
Circuit components: cell or battery, key (switch), rheostat, ammeter connected in series, voltmeter connected in parallel across the resistor.
Procedure: measure total V and I, find R = V/I by Ohm's law, compare with the calculated R_e. The small difference R_e - R is experimental error.

B. Minor experiments (Section B, 4 marks each)

P-Minor 1. Spring constant from a load-extension graph

Hang the spring, add loads (weight W = mg), measure extension x each time. Plot load (force) on x-axis, extension on y-axis.
Hooke's law: F = kx, so extension is proportional to load up to the limit of proportionality (the point where the graph stops being a straight line). Slope of the extension-load graph = extension per unit load = 1/k. Slope of force-extension (force on y) = k.
Use a force meter (newton meter) to measure weight. Do not overload past the limit.

P-Minor 2. Centre of gravity of a plane lamina by plumb line

Make three small holes near the edge. Hang the lamina freely from a pin through one hole, hang the plumb line from the same pin, mark the vertical line on the lamina. Repeat with the other holes. The lines meet at one point: the centre of gravity.
Check: the lamina balances horizontally on a pencil tip at that point.

P-Minor 3. Volume of an irregular stone by displacement, and its density

Measure mass m on an electronic balance. Fill a measuring cylinder with some water, read V₁, tie the stone with thread, lower it gently, read V₂. Volume V = V₂ - V₁. Density = m/V (g/cm³ or kg/m³).
Read the bottom of the meniscus at eye level, no air bubbles, no splashing.

P-Minor 4. Laws of reflection using a plane mirror

Fix a plane mirror upright on white paper, draw its line. Fix two pins P₁ and P₂ to give the incident ray. Look into the mirror and fix P₃ and P₄ in line with the images. Draw the normal, measure angle of incidence i and angle of reflection r.
Laws: (1) angle of incidence = angle of reflection, (2) incident ray, reflected ray and normal lie in one plane.

P-Minor 5. Refraction through a glass slab and refractive index

Place the slab on paper, trace it. Fix pins P₁, P₂ on one side, look through the other side and fix P₃, P₄ in line with their images. Join P₃P₄ to the edge, join the entry and exit points. Draw the normal at the entry point, measure angle of incidence i and angle of refraction r.
n = sin i / sin r (glass is about 1.5). The emergent ray is parallel to the incident ray and is shifted sideways: this is the lateral shift. Ray bends towards the normal when entering glass (denser).

P-Minor 6. Critical angle of a prism

Critical angle C = the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90 degrees. Total internal reflection happens when the angle of incidence is greater than C. Conditions: ray goes from denser to rarer medium, and the angle of incidence exceeds C.
Use a right-angled isosceles (45-45-90) glass prism. Send rays through the prism, rotate until the emergent ray just disappears along the surface, measure that angle. For glass C is about 42 degrees. sin C = 1/n.

P-Minor 7. V-I characteristics of a resistor (Ohm's law)

Ammeter in series, voltmeter across the resistor, vary current with the rheostat, record V and I. Plot V (y) against I (x): a straight line through the origin. Slope = R = V/I.
Ohm's law: V is proportional to I at constant temperature. A filament lamp gives a curve (resistance rises as it heats). A diode conducts in one direction only.

P-Minor 8. Potential difference across a wire against its length

Pass a constant current through a uniform wire fixed on a metre scale. Measure V across lengths of 20, 40, 60, 80, 100 cm. V is directly proportional to length l, so V against l is a straight line through the origin. Reason: R = rho l / A, so V = IR grows with l. Keep the current constant using the rheostat and switch it off between readings so the wire does not heat.

C. Model paper solved (Physics, 20 marks)

Q.1 Series combination of resistances (6 marks)

i. Circuit diagram (2). Draw: battery (cell symbol) and key in series with R₁, R₂ and an ammeter A in one loop. Connect voltmeter V₁ in parallel across R₁, V₂ in parallel across R₂, and a voltmeter V across the pair. (Sketch only. In your answer draw it neatly with standard symbols and label V1 across R1, V2 across R2, V across both.)

ii. Table (3). R_e = R₁ + R₂. V = V₁ + V₂. I = V₁/R₁ (same in series). R = V/I.

Obs	V1 (V)	V2 (V)	R1 (ohm)	R2 (ohm)	Re (ohm)	V (V)	I (A)	R = V/I (ohm)
1	2	10	10	50	60	12	0.2	60
2	6	10	60	100	160	16	0.1	160
3	4.8	12	80	200	280	16.8	0.06	280

Check: V₁/R₁ = V₂/R₂ in every row (2/10 = 10/50 = 0.2; 6/60 = 10/100 = 0.1; 4.8/80 = 12/200 = 0.06), so the current is the same through both resistors, as it must be in series.

iii. (1) The equivalent resistance increases (it becomes R₁ + R₂ + R₃) and, for the same voltage, the current decreases.

Q.2 Ball rolling down an angle iron (6 marks)

i. Apparatus (1): angle iron, steel ball, stop watch, metre rule, wooden block or stand (to raise one end), chalk or marker.

ii. Table (2). Mean time t = (t₁ + t₂)/2, velocity = distance / t.

Obs	Distance (cm)	t1 (s)	t2 (s)	Mean t (s)	Velocity (cm/s)
1	200	4.4	4.6	4.50	44.4
2	180	4.1	4.0	4.05	44.4
3	160	3.9	3.3	3.60	44.4
4	140	3.2	3.1	3.15	44.4
5	120	2.8	2.6	2.70	44.4
6	100	2.5	2.0	2.25	44.4

iii. Graph (2). Plot time t (x-axis, 0 to 5 s) and distance d (y-axis, 0 to 200 cm). Points: (2.25, 100), (2.70, 120), (3.15, 140), (3.60, 160), (4.05, 180), (4.50, 200). They lie on one straight line through the origin, slope = 44.4 cm/s. Give a title, label both axes with units, choose a scale that fills the page.

iv. (1) If the angle of inclination is reduced, the acceleration of the ball decreases, so its speed is less and it takes more time to cover the same distance.

Q.3 Refraction through a glass slab (4 marks)

i. (2) Draw the normal (a line perpendicular to the surface) at the point where the ray enters the slab. Angle of incidence i = angle between the incident ray (in air) and the normal. Angle of refraction r = angle between the refracted ray (in glass) and the normal. Measured on the printed figure with a protractor: i is about 60 degrees and r is about 21 degrees.
ii. (2) n = sin i / sin r = sin 60 / sin 21 = 0.866 / 0.358 = about 2.4.

The printed figure is only a rough sketch, and the angles scale off the image only approximately, so n comes out higher than real glass (about 1.5). In the exam the marks go for: drawing the normal, correct i and r from your own measurement, writing n = sin i / sin r, substituting, and the unit-free answer. Show these steps. (As a check, i = 60 and r = 35 would give n = 1.5.)

Q.4 Force-extension graph of a helical spring (4 marks)

i. (1) Independent variable: force (load), on the x-axis. Dependent variable: extension, on the y-axis.
ii. (2) Slope = (y_B - y_A) / (x_B - x_A) = (2.0 - 1.5) cm / (200 - 150) dynes = 0.5 / 50 = 0.01 cm per dyne.
iii. (1) The slope is the extension per unit load, which is 1/k, the reciprocal of the spring constant. So k = 1 / 0.01 = 100 dynes per cm.