Class 11 Physics Notes Chapter 10 (Chapter 10) – Lab Manual (English) Book
Detailed Notes with MCQs of the key experiments typically covered around Chapter 10 in your Physics Lab Manual, which deal with the Properties of Bulk Matter. These experiments are fundamental and often form the basis for questions in various government exams. Pay close attention to the principles, formulae, precautions, and sources of error.
Chapter 10: Properties of Bulk Matter - Key Experiments (Notes for Government Exams)
Experiment 1: To determine Young's Modulus (Y) of the material of a given wire using Searle's Apparatus.
- Aim: To find the Young's Modulus of Elasticity (Y) for the material of a wire.
- Concept:
- Elasticity: The property of a material to regain its original shape and size after the removal of deforming forces.
- Stress: The internal restoring force set up per unit area of cross-section of a deformed body.
- Longitudinal Stress = Force (F) / Area (A) = Mg / (πr²)
- Unit: N/m² or Pascal (Pa)
- Dimension: [ML⁻¹T⁻²]
- Strain: The fractional change in configuration (dimension) of the body.
- Longitudinal Strain = Change in Length (ΔL) / Original Length (L)
- Unit: Dimensionless
- Dimension: [M⁰L⁰T⁰]
- Hooke's Law: Within the elastic limit, stress is directly proportional to strain. (Stress ∝ Strain)
- Young's Modulus (Y): The ratio of longitudinal stress to longitudinal strain, within the elastic limit. It measures the material's resistance to elongation.
- Y = Longitudinal Stress / Longitudinal Strain
- Apparatus:
- Searle's Apparatus: Consists of two identical wires (Reference/Compensating Wire and Experimental Wire) suspended from a rigid support. Frames are attached to the bottom of the wires. One frame carries a spirit level, and the other carries a micrometer screw whose tip touches the spirit level frame.
- Other: Slotted weights (for applying load), metre scale (for measuring L), micrometer screw gauge (for measuring wire diameter 'd').
- Formula Used:
- Y = (MgL) / (A * ΔL) = (MgL) / (πr² * ΔL)
- Where:
- M = Mass added to the experimental wire (causing extension) (kg)
- g = Acceleration due to gravity (m/s²)
- L = Original length of the experimental wire (m)
- r = Radius of the wire (d/2) (m)
- A = Cross-sectional area of the wire (πr²) (m²)
- ΔL = Mean extension or elongation of the wire for mass M (m)
- Procedure Highlights & Measurements:
- Measure original length L (from fixed support to frame).
- Measure diameter 'd' at several points and orientations using a screw gauge; calculate mean radius r = d/2.
- Apply a dead load to keep wires straight. Note initial micrometer reading (for spirit level centered).
- Add load (M) in steps (e.g., 0.5 kg) to the experimental wire only. Adjust micrometer to re-center the spirit level and record reading.
- Take readings for both increasing and decreasing loads.
- Calculate the mean extension (ΔL) corresponding to a specific load M (often the difference between readings for a higher and lower load is used).
- Why Two Wires? The reference wire compensates for:
- Thermal expansion/contraction due to temperature changes.
- Yielding of the support.
- Precautions:
- Wires should be long, thin, identical, and free from kinks.
- Apply a dead load initially.
- Load/unload gently.
- Wait after changing load before taking readings (for elastic after-effect).
- Measure diameter 'd' accurately (error in 'r' is squared in the formula).
- Take readings for both increasing and decreasing loads (minimizes backlash error).
- Do not exceed the elastic limit of the wire.
- Sources of Error:
- Error in measurement of L and especially 'r' (or 'd').
- Backlash error in the micrometer screw.
- Non-uniform wire cross-section.
- Kinks in the wire.
- Yielding of support (if not compensated).
- Elastic after-effect (if readings taken too quickly).
Experiment 2: To determine the Surface Tension (T) of water by Capillary Rise Method.
- Aim: To measure the surface tension of water at room temperature.
- Concept:
- Surface Tension (T): The property of a liquid by virtue of which its free surface behaves like a stretched elastic membrane, tending to minimize its surface area. It's defined as the force per unit length acting perpendicular to an imaginary line drawn on the liquid surface.
- Unit: N/m
- Dimension: [MT⁻²]
- Capillary Rise: The phenomenon of rise or fall of a liquid in a narrow tube (capillary) compared to the surrounding level. It's due to surface tension and the forces of cohesion and adhesion.
- Angle of Contact (θ): The angle between the tangent to the liquid surface at the point of contact and the solid surface inside the liquid. For pure water and clean glass, θ ≈ 0°, so cos θ ≈ 1.
- Apparatus: Capillary tube of uniform bore, travelling microscope, beaker, clamp stand, thermometer, clean water.
- Formula Used:
- T = (r * h * ρ * g) / (2 * cos θ)
- For water and clean glass, θ ≈ 0°, cos θ ≈ 1. So, T = (r h ρ g) / 2
- Where:
- r = Inner radius of the capillary tube (m)
- h = Height of the liquid rise in the capillary above the free surface in the beaker (m)
- ρ = Density of the liquid (kg/m³)
- g = Acceleration due to gravity (m/s²)
- Procedure Highlights & Measurements:
- Ensure the capillary tube is clean.
- Measure the inner diameter of the tube using a travelling microscope; calculate radius 'r'.
- Mount the tube vertically with its lower end dipped in water.
- Measure the height 'h' of the water column in the capillary (from the bottom of the meniscus to the free surface level outside) using a travelling microscope.
- Precautions:
- Capillary tube must be clean.
- Tube must be held vertically.
- Measure 'h' carefully, avoiding parallax error. Use travelling microscope for accuracy.
- Measure temperature as surface tension depends on it (decreases with increasing temperature).
- Sources of Error:
- Non-uniform bore of the capillary tube.
- Tube not vertical.
- Impurities in water or dirty tube (affects T and θ).
- Error in measuring 'r' and 'h'.
- Temperature fluctuations.
Experiment 3: To determine the Coefficient of Viscosity (η) of a given viscous liquid by measuring the terminal velocity of a spherical body (Stokes' Law).
- Aim: To find the coefficient of viscosity of a highly viscous liquid (like glycerine or castor oil).
- Concept:
- Viscosity (η): The property of a fluid (liquid or gas) by virtue of which it opposes the relative motion between its adjacent layers. It's like internal friction in fluids.
- Unit: Poiseuille (Pl) or Pa·s (SI); dyne·s/cm² or Poise (CGS). 1 Pl = 10 Poise.
- Dimension: [ML⁻¹T⁻¹]
- Stokes' Law: The viscous drag force (F<0xE1><0xB5><0xBD>) acting on a small sphere moving with terminal velocity (v<0xE1><0xB5><0x9C>) through a homogeneous viscous fluid is given by F<0xE1><0xB5><0xBD> = 6πηrv<0xE1><0xB5><0x9C>. This law is valid for low Reynolds numbers (laminar flow).
- Terminal Velocity (v<0xE1><0xB5><0x9C>): The constant maximum velocity acquired by a body falling through a viscous fluid, when the net force on the body becomes zero (Viscous Drag + Buoyant Force = Gravitational Force).
- Apparatus: Tall transparent cylindrical jar filled with the viscous liquid, small spherical balls (e.g., steel ball bearings), micrometer screw gauge, stop watch, metre scale/thread, thermometer.
- Formula Used:
- At terminal velocity: Weight = Buoyant Force + Viscous Drag
- (4/3)πr³ρg = (4/3)πr³σg + 6πηrv<0xE1><0xB5><0x9C>
- Rearranging gives: η = [2 r² (ρ - σ) g] / (9 v<0xE1><0xB5><0x9C>)
- Where:
- r = Radius of the spherical ball (m)
- ρ = Density of the material of the sphere (kg/m³)
- σ = Density of the viscous liquid (kg/m³)
- g = Acceleration due to gravity (m/s²)
- v<0xE1><0xB5><0x9C> = Terminal velocity of the sphere (m/s)
- Procedure Highlights & Measurements:
- Measure the radius 'r' of the sphere using a screw gauge.
- Mark two points (A and B) well below the surface in the liquid column. Measure the distance (S) between A and B.
- Drop the sphere gently and centrally into the liquid.
- Start the stopwatch when the sphere crosses mark A and stop it when it crosses mark B (ensure it has attained terminal velocity before A).
- Calculate terminal velocity v<0xE1><0xB5><0x9C> = S / time taken. Repeat for mean value.
- Measure the temperature of the liquid (viscosity is highly temperature-dependent).
- Use known values or measure densities ρ and σ.
- Precautions:
- Liquid column should be wide and tall enough to minimize wall effects and allow terminal velocity attainment.
- Sphere should be small and smooth.
- Drop the sphere gently and along the axis of the cylinder.
- Ensure terminal velocity is reached before timing starts (start timing well below the surface).
- Keep the liquid temperature constant and record it.
- Sources of Error:
- Error in measuring 'r' (significant as r²).
- Error in measuring time and distance for v<0xE1><0xB5><0x9C>.
- Sphere not falling centrally.
- Liquid temperature not constant (viscosity decreases significantly with increasing temperature).
- Wall effects (if the jar is not wide enough).
- Sphere may not be perfectly spherical or smooth.
Multiple Choice Questions (MCQs)
-
In Searle's apparatus experiment, the use of a reference wire primarily compensates for:
a) Error in measuring length L
b) Error in measuring diameter d
c) Effects of temperature changes and support yielding
d) Backlash error in the micrometer -
The dimensional formula for Young's Modulus (Y) is:
a) [MLT⁻²]
b) [ML⁻¹T⁻²]
c) [ML⁻²T⁻²]
d) [ML⁻¹T⁻¹] -
If the radius of the wire used in Searle's apparatus is doubled, keeping other factors constant, the Young's Modulus of the material will:
a) Become double
b) Become half
c) Become four times
d) Remain unchanged -
In the capillary rise method for surface tension, if the capillary tube is inclined at an angle α to the vertical, the vertical height 'h' of the liquid column will:
a) Increase
b) Decrease
c) Remain the same
d) Become zero -
The SI unit of coefficient of viscosity (η) is:
a) Poise
b) N/m²
c) Pa·s
d) N·m -
According to Stokes' Law, the viscous drag force is directly proportional to:
a) Radius of the sphere (r)
b) Square of the radius (r²)
c) Terminal velocity (v<0xE1><0xB5><0x9C>)
d) Both (a) and (c) -
A key precaution while measuring the diameter of the wire for Young's Modulus experiment is:
a) Measure only at one point
b) Measure using a metre scale
c) Measure at multiple points and orientations using a screw gauge
d) Measure after applying the maximum load -
Terminal velocity is reached when:
a) Viscous force equals the weight of the body
b) Buoyant force equals the viscous force
c) Net force on the body is zero
d) The body stops moving -
For pure water in contact with clean glass, the angle of contact (θ) is approximately:
a) 90°
b) 180°
c) 45°
d) 0° -
Which measurement error has the most significant impact on the calculated value of viscosity (η) using Stokes' Law formula η = [2 r² (ρ - σ) g] / (9 v<0xE1><0xB5><0x9C>)?
a) Error in measuring g
b) Error in measuring terminal velocity v<0xE1><0xB5><0x9C>
c) Error in measuring density σ
d) Error in measuring radius r
Answer Key for MCQs:
- c
- b
- d (Young's Modulus is a material property)
- c (The length along the tube 'l' will increase such that l cos α = h, but the vertical height 'h' depends only on r, T, ρ, g)
- c
- d
- c
- c
- d
- d (Because 'r' is squared in the formula)
Study these notes thoroughly. Focus on understanding the 'why' behind each step and formula. Good luck with your preparation!