SMA Physics

To determine the internal diameter, external diameter, and depth of a hollow cylindrical calorimeter/beaker and calculate its internal volume using Vernier Callipers.

Vernier Callipers, cylindrical calorimeter/beaker, spherical bob, magnifying lens.

A Vernier Calliper operates on the principle that $N$ divisions of the sliding Vernier Scale coincide with $(N - 1)$ divisions of the stationary Main Scale.

1. Examine the Vernier Callipers to determine its Least Count ($0.01\text{ cm}$).
2. Bring jaws $A$ and $B$ into contact to inspect zero error. If zero of Vernier scale lies to the right of main scale zero, error is positive; if to the left, error is negative.
3. To measure external diameter ($D_e$), place the cylinder between external jaws $A$ and $B$ and tighten gently using the clamp screw.
4. Record the main scale reading immediately preceding the vernier zero mark.
5. Observe which vernier division aligns exactly with any main scale graduation using a magnifying lens.
6. Repeat readings at 3 different cross-sections at mutually perpendicular directions to eliminate ellipticity.
7. To measure internal diameter ($D_i$), place upper jaws $C$ and $D$ inside the hollow cylinder and expand until snug.
8. To measure depth ($d$), insert the thin metallic depth strip vertically until it touches the cylinder base while the calliper edge rests flat on the rim.
9. Compute mean internal diameter and depth, then calculate internal volume.

• Do not apply excessive pressure on the jaws; turn the adjusting screw smoothly to avoid bending or deforming the jaws.
• Always record observations at three mutually perpendicular diameters to account for non-uniform circular cross-sections.
• View the vernier alignment directly perpendicular to the scale to avoid parallax error.
• Always apply zero correction with proper algebraic sign ($TR = \text{Observed} - \text{Zero Error}$).

To measure the diameter of a given wire and thickness of a given sheet using a micrometer screw gauge and calculate its cross-sectional area and volume.

Screw gauge ($0-25\text{ mm}$, $LC = 0.001\text{ cm}$), thin copper/nichrome wire, metallic sheet, half-meter rule.

The micrometer screw gauge is based on the principle of the screw: linear advancement along the axis is directly proportional to circular rotation of the thimble head.

1. Determine pitch by rotating the thimble 5 complete turns and observing linear progression along the sleeve scale.
2. Determine least count ($LC = 0.001\text{ cm}$).
3. Rotate the ratchet stop until anvil and spindle faces meet. Inspect zero error against reference datum line.
4. Place the wire between anvil and spindle. Turn the ratchet head until it slips with 3 distinct audible clicks.
5. Note the Pitch Scale Reading (PSR) and the Circular Scale Division (CSR) aligned with the reference line.
6. Repeat measurements at 5 equidistant locations along the wire, taking two perpendicular diameters at each spot.
7. Measure total length $L$ with a meter scale and compute wire volume.

• Always advance and tighten the screw using the ratchet stop, never the knurled thimble directly, to avoid crushing the specimen or stripping screw threads.
• Turn the screw only in one direction during measurement to prevent backlash error caused by mechanical thread wear.
• Clean the planar faces of both anvil and spindle before zero error inspection.

To determine the radius of curvature of a given spherical surface (convex watch glass/concave mirror) using a spherometer.

Spherometer, plane glass plate, spherical watch glass/convex mirror, sheet of white paper, sharp pencil, millimeter rule.

A spherometer measures the sagitta (height of bulge or depth of depression $h$) of a spherical cap supported on an equilateral triangular base of leg distance $l$.

1. Press the spherometer legs gently onto paper to produce 3 prong indentations forming an equilateral triangle. Measure distances $l_1, l_2, l_3$ and compute mean $l$.
2. Place the spherometer on a flat plane glass slab. Rotate central screw downwards until its tip just touches the glass without lifting the three outer legs.
3. Record the plane zero vertical scale and circular head readings.
4. Place the spherometer centrally on the convex/concave spherical surface.
5. Turn the screw until the central tip touches the apex of the spherical surface.
6. Calculate sagitta $h = |\text{Surface Reading} - \text{Plane Zero Reading}|$.
7. Substitute $l$ and $h$ into formula to calculate radius of curvature $R$.

• Ensure the central screw does not press so hard that the outer legs lift off the surface. Use a thin paper strip under each leg to test contact.
• Rotate the micrometer screw strictly in one direction to eliminate backlash error.

To determine the volume of a given irregular thin lamina using millimeter graph paper and a micrometer screw gauge.

Irregular lamina (cardboard/metallic plate), $1\text{ mm}$ graph sheet, sharp pencil, micrometer screw gauge.

Volume of any regular or irregular prismatic sheet is the product of its surface area $A$ and uniform thickness $t$.

1. Place the irregular lamina flat on a sheet of millimeter graph paper.
2. Trace its perimeter boundary carefully using a very sharp pencil held perpendicularly.
3. Count all complete squares enclosed within the boundary ($N_1$).
4. Count all boundary squares that have half or more than half their area inside the contour ($N_2$). Ignore squares with less than half area inside.
5. Compute total surface area $A$.
6. Measure thickness $t$ at 5 widely separated locations using a calibrated screw gauge with zero error correction applied.
7. Calculate total volume $V = A \times t$.

• Use an extremely sharp 2H pencil so that boundary line thickness does not introduce area bias.
• Ensure the lamina is perfectly flat without warping or bent corners.

To determine the mass of a given body using a physical beam balance by the method of resting point oscillations.

Physical balance, analytical weight box with forceps, fractional milligram weights, spirit level, plumb line, unknown body.

A beam balance operates on the principle of moments: equilibrium occurs when clockwise moment equals counter-clockwise moment about the central fulcrum.

1. Level the balance using foot screws until the plumb line aligns with the pointed cone index.
2. Release the beam arresting knob and determine the Zero Resting Point (ZRP) by recording three consecutive turning points of the pointer on the graduated scale.
3. Arrest the beam. Place the unknown body in the left pan.
4. Place standard gram weights in the right pan using forceps. Always arrest the beam before changing weights!
5. Add fractional milligram weights until pointer swings symmetrically across scale.
6. Determine resting point with weights ($RP$). Calculate exact mass with oscillation correction.

• Always arrest the beam completely before adding or removing weights to protect delicate agate knife-edges.
• Handle weights strictly with clean bone-tipped forceps; finger oil/sweat alters fractional milligram accuracy.
• Keep glass doors shut during oscillation readings to eliminate air draft currents.

To determine the weight of a given body using the Parallelogram Law of Vectors on Gravesand's apparatus.

Gravesand's vertical drawing board, 2 low-friction pulleys, slotted weights with hangers, white paper, drawing pins, mirror strip, thread, unknown weight.

If two concurrent forces $\vec{P}$ and $\vec{Q}$ acting at a point are represented in magnitude and direction by adjacent sides of a parallelogram, their resultant $\vec{R}$ is represented by the diagonal passing through their common junction.

1. Fix drawing paper to vertical board. Ensure pulleys move without friction.
2. Pass thread over pulleys. Suspend known weights $P$ and $Q$ on sides and unknown weight $W$ from central junction knot $O$.
3. Adjust weights until knot $O$ rests near center of board without touching paper.
4. Mark directions of all three threads using plane mirror parallax method (align thread with its reflection).
5. Choose suitable vector scale ($1\text{ cm} = 50\text{ g-wt}$) and draw vectors $\vec{OA} = P$ and $\vec{OB} = Q$.
6. Complete parallelogram $OACB$ and measure length of diagonal $OC$.
7. Calculate unknown weight $W = OC \times \text{Scale}$. Compare with spring balance reading.

• Pulleys must be frictionless and oiled.
• Threads must remain parallel to drawing board without rubbing against paper.

To study the variation of time period $T$ with length $L$ of a simple pendulum, plot an $L-T^2$ graph, determine acceleration due to gravity $g$, and find length of a second's pendulum.

Heavy metallic spherical bob with hook, light inextensible cord, split cork, rigid retort stand, vernier callipers, meter scale, precision digital stopwatch.

For small angular displacement ($\theta \le 4^\circ$), the simple pendulum executes Simple Harmonic Motion (SHM).

1. Measure bob diameter with Vernier Callipers to get radius $r$.
2. Clamp cord firmly between two halves of split cork. Adjust effective length $L = l + r + e$ to $60\text{ cm}$.
3. Pull bob aside by small angle ($< 4^\circ$) and release without imparting spin.
4. Start stopwatch as bob crosses central equilibrium line. Measure time for 20 complete oscillations twice.
5. Repeat for lengths $70, 80, 90, 100, 110\text{ cm}$.
6. Compute period $T = t / 20$, $T^2$, and $L/T^2$. Plot $L$ vs $T^2$ linear graph and deduce $g$.

• Angular amplitude must remain under $4^\circ$ so that $\sin\theta \approx \theta$.
• Oscillations must be planar without conical or spinning motion.

To study the relationship between the force of limiting friction and normal reaction, and determine the coefficient of static friction $\mu_s$ between a wooden block and a horizontal table.

Horizontal wooden bench with frictionless pulley, wooden block with hook, pan, slotted weights ($50\text{ g}, 100\text{ g}$), spring balance, thread.

The maximum opposing frictional force before a body begins to slide is the limiting friction $F_s$, directly proportional to normal reaction $R$.

1. Weigh the wooden block and scale pan using a spring balance.
2. Place block on clean horizontal bench. Attach thread passing horizontally over pulley to suspended pan.
3. Add small weights to pan and tap bench gently until block just begins to slide. Note total pan mass.
4. Add $50\text{ g}, 100\text{ g}, 150\text{ g}, 200\text{ g}$ atop the block to increase normal reaction $R$.
5. Record corresponding limiting pulling force $F$. Plot $F$ vs $R$ and determine slope $\mu_s$.

• The string connecting block to pulley must be strictly horizontal.
• Always tap the bench gently to overcome initial contact stickiness.

To study the downward force along an inclined plane acting on a roller due to gravity and verify its relationship with $\sin\theta$.

Inclined plane with protractor and pulley, heavy metallic roller, spring balance, weight pan, slotted weights, light cord.

A mass $m$ placed on an incline tilted at angle $\theta$ experiences gravitational components:

1. Weigh roller and pan. Set inclined plane angle $\theta = 20^\circ$.
2. Attach cord to roller, pass over top pulley, and attach to pan.
3. Determine weight $W_1$ needed in pan for roller to move up with constant speed.
4. Determine weight $W_2$ in pan when roller moves down with constant speed.
5. Mean downward force $F = \frac{W_1 + W_2}{2}$ eliminates rolling friction.
6. Repeat for $\theta = 30^\circ, 40^\circ, 45^\circ, 50^\circ$. Plot $F$ vs $\sin\theta$.

• Cord must be parallel to the plane surface.
• Pulley must be frictionless and clean.

To determine resistance per unit length of a given wire by plotting a graph of potential difference versus current, and calculate specific resistance (resistivity) of its material.

Resistance wire (Constantan/Nichrome), DC power supply ($0-6\text{ V}$), DC ammeter ($0-1.5\text{ A}$), DC voltmeter ($0-3\text{ V}$), rheostat, plug key, connecting wires, screw gauge, meter scale.

Ohm's Law: Electric current $I$ flowing through a conductor is directly proportional to potential difference $V$ across its ends, provided physical conditions (temperature, strain) remain constant.

1. Clean wire terminals with sandpaper. Connect battery, key, rheostat, ammeter, and resistance wire in series.
2. Connect voltmeter in parallel across the resistance wire.
3. Insert key and adjust rheostat so that ammeter and voltmeter show measurable deflections.
4. Record ammeter current $I$ and voltmeter voltage $V$.
5. Shift rheostat slider to obtain 6 distinct sets of $V$ and $I$ values.
6. Measure wire length with meter rule and diameter with screw gauge.
7. Plot $V$ vs $I$ graph and compute slope $R$ and resistivity $\rho$.

• Keep the plug key open between readings to prevent Joule heating ($I^2Rt$), which increases resistance.
• Connect voltmeter strictly in parallel and ammeter in series with correct polarity ($+$ to $+$).

To find the resistance of a given wire using a meter bridge and determine the specific resistance (resistivity) of its material.

Meter bridge ($100\text{ cm}$ slide wire), center-zero galvanometer, Leclanché/DC cell, resistance box ($1-100\,\Omega$), sliding jockey, unknown resistance wire, screw gauge, meter scale.

The meter bridge is a practical laboratory realization of the Wheatstone bridge null deflection principle.

1. Connect standard resistance box $R$ in left gap and unknown coil $X$ in right gap. Connect battery across end brass terminals $A$ and $C$, and galvanometer between central terminal $B$ and jockey.
2. Test connection by touching jockey at $l=5\text{ cm}$ and $l=95\text{ cm}$; galvanometer needle must deflect in opposite directions.
3. Take out suitable resistance $R$ from box ($2-6\,\Omega$). Slide jockey gently to locate null deflection point ($I_g = 0$).
4. Record balancing length $l$ from zero end.
5. Repeat for 5 different values of $R$ ensuring balance point remains between $35\text{ cm}$ and $65\text{ cm}$.
6. Measure wire diameter with screw gauge and calculate resistivity $\rho$.

• Jockey must be touched lightly onto wire, never dragged or scraped (scraping distorts wire diameter uniformity).
• Keep balancing length near $50\text{ cm}$ for maximum bridge sensitivity and minimal percentage error.

To determine the unknown resistance of a resistor by setting up a 4-arm Wheatstone's bridge network and verifying null condition.

Wheatstone bridge quadrilateral assembly with ratio arms ($P, Q$), adjustable resistance arm ($R$), unknown arm ($S$), galvanometer, DC battery, key.

In a closed bridge network $ABCD$, when potential at junction $B$ equals potential at junction $D$, no current flows through galvanometer ($I_g = 0$).

1. Set ratio arms $P$ and $Q$ to desired ratio (e.g. $10\,\Omega : 10\,\Omega$ or $100\,\Omega : 10\,\Omega$).
2. Connect unknown resistor in arm $S$.
3. Depress battery key $K_1$ first, then tap galvanometer key $K_2$.
4. Adjust resistance $R$ until galvanometer deflection drops to exactly zero.
5. Compute unknown resistance $S = R(Q/P)$.

• Always close battery key first, then galvanometer key to prevent transient inductive deflection kick.