CONTENTS. Vernier Calipers. Screw Gauge. Simple Pendulum 7. Moment Bar 9. Convex Lens Appendix
Vernier Calipers Exp. No: Date: Aim (i) To nd the volume of the given cylinder by measuring its length and diameter (ii) To nd the volume of the given rectangular block by measuring its length, breadth and thickness Apparatus Vernier caliper, metallic cylinder and rectangular block Principle Vernier caliper consists of a metal scale graduated in mm which forms the main scale. It has a xed jaw J at one end and a movable jaw J provided with a vernier scale which slides over the main scale. The least count of the vernier is the smallest distance that can be measured with it and it can be calculated using the equation, Least count of vernier (LC) Value of one main scale division (MSD) Number of divisions on the vernier scale () Total reading MSR + (V SR LC) () where MSR is the main scale reading and VSR is the vernier scale reading. If l is the length of the cylinder and r is the radius of the cylinder, Volume of the cylinder, V πr l () If l is the length, b is the breadth and t is the thickness of the rectangular block, Volume of the rectangular block, V lbt () Procedure The value of one main scale division and number of divisions on the vernier scale are noted. The least count of the vernier is calculated using equation (). To nd the volume of the cylinder The given cylinder is gently gripped lengthwise between the jaws of the vernier caliper. The main scale reading (MSR) just before the zero of the vernier scale is noted. The vernier scale reading (VSR) coinciding with some division on the main scale is also noted. The length of the cylinder is then calculated using equation (). The experiment is repeated ve times and the average value of the length of the cylinder is calculated.
The cylinder is gently gripped diameter-wise between the jaws. Main scale reading and vernier scale reading are noted and the diameter of the cylinder is then calculated using equation (). The experiment is repeated ve times and the average value of the diameter of the cylinder is calculated. The half of the mean diameter gives the radius of the cylinder. The volume of the cylinder is then calculated using equation (). To nd the volume of the rectangular block The given rectangular is gently gripped lengthwise between the jaws of the vernier caliper. The main scale reading (MSR) just before the zero of the vernier scale is noted. The vernier scale reading (VSR)coinciding with some division on the main scale is also noted. The length of the rectangular block is then calculated using equation (). The experiment is repeated ve times and the average value of the length of the rectangular block is calculated. The same procedure is repeated to nd the breadth and thickness of the rectangular block. The volume of the rectangular block is then calculated using equation (). Result Volume of the given cylinder m Volume of the given rectangular block m Observations and Calculations Value of one main scale division Total number of divisions on the vernier scale Least count of vernier (LC) Value of one main scale division (MSD) Number of divisions on the vernier scale (i) To nd the volume of the cylinder Dimension Length of the cylinder Diameter of the cylinder Trial No MSR () VSR Total Reading MSR + (VSR x LC) () Mean ()
Length of the cylinder (l) Diameter of the cylinder (D) Radius of the cylinder (r) D Volume of the cylinder πr l 0 6 m (i) To nd the volume of the rectangular block Dimension Length of the rectangular block Breadth of the rectangular block Thickness of the rectangular block Trial No MSR () VSR Total Reading MSR + (VSR x LC) () Mean () Length of the rectangular block (l) Breadth of the rectangular block (b) Thickness of the rectangular block (t) Volume of the rectangular block (V) lbt 0 6 m
Screw Gauge Exp. No: Date: Aim (i) To nd the volume of the given wire by measuring its length and diameter (ii) To nd the volume of the given glass plate by measuring its thickness and area Apparatus Screw Gauge, metal wire and glass plate Principle Screw gauge works on the simple principle of converting small distances into larger ones by measuring the rotation of the screw. When the head of the screw gauge is rotated, the distance moved by the screw for every complete rotation is a constant called pitch of the screw. Distance moved Pitch of the screw gauge (P) Number of rotations Pitch (P) Least count of the screw gauge (LC) Number of divisions on the head scale (N) () () Total reading P SR + (Corrected HSR LC) () where PSR is the pitch scale reading and HSR is the head scale reading. If l is the length of the wire and r is the radius of the wire, Volume of the wire, V πr l () If t is the thickness and A is the area of the glass plate, Volume of the glass plate, V At () Procedure The pitch, least count and zero error of the screw gauge are determined rst. The head of the screw gauge is given six complete rotations and distance moved by head over the pitch scale is noted. The pitch of the screw gauge is calculated using equation (). The number of divisions on the head scale is noted and least count of the screw gauge is calculated using equation (). To nd the zero error, the screw head is rotated until the two plane faces are just in contact. If the zero of the head scale coincides with the reference line on the pitch scale, the instrument has no zero error and hence, no zero correction. If the zero of the head scale is above the reference line (say by divisions), the zero error is - div and zero correction is + div. If the zero of the head scale is below the reference line (say by divisions), the zero error is + div and zero correction is - div.
This correction is to be added to the observed head scale reading (HSR) when the measurement is taken. To nd the volume of the wire The diameter of the wire is measured by gently gripping the wire between the plane faces of the screw gauge. Pitch scale reading (PSR)just before the head of the screw gauge is noted. Head scale reading (HSR) coinciding with the reference line on the pitch scale is also noted. The diameter of the wire is then calculated using equation (). The experiment is repeated ve times and the average value of the diameter of the wire is calculated. The half of the mean diameter gives the radius of the wire. The length of the wire is measured using a meter scale. The volume of the wire is then calculated using equation (). To nd the volume of the glass plate The given glass plate is gently gripped between the plane faces of the screw gauge. The pitch scale reading and head scale reading are noted. The thickness of the glass plate is then calculated using equation (). The experiment is repeated ve times and the average value of the thickness of the glass plate is calculated. To nd the area of the glass plate, its outline is taken on a graph paper and the number of millimeter squares enclosed in it is counted. The volume of the glass plate is then calculated using equation (). Result Volume of the given wire m Volume of the given glass plate m Observations and Calculations Value of one pitch scale division Distance moved for 6 rotations of the head Pitch of the screw gauge (P) mm mm Distance moved Number of rotations Total number of divisions on the head scale (N) Least count of screw gauge (LC) P N mm mm
Dimension Diameter of the wire Thickness of the glass plate Trial No PSR (mm) HSR Corrected HSR Total Reading PSR + (Corrected HSR x LC) (mm) Mean (mm) (i) To nd the volume of the wire Length of the wire (l) Diameter of the wire (D) mm mm Radius of the wire (r) D Volume of the wire mm πr l mm 0 9 m (ii) To nd the volume of the glass plate Area of the glass plate (A) mm Thickness of the glass plate (t) mm Volume of the glass plate (V) At mm 0 9 m 6
Simple Pendulum Exp. No: Date: Aim (i) To determine the acceleration due to gravity (g) at the place (ii) To determine the length of the seconds pendulum from (l, T ) graph Apparatus Simple pendulum, stop clock and meter scale Principle The simple pendulum consists of a small metallic bob suspended by a light string. The length of the pendulum (l) is the distance between the centre of the bob and the point of suspension. The period (T) of the pendulum is the time taken to complete one oscillation. The relation between length of the pendulum, its period and acceleration due to gravity is given by T π l g ) ( l T π g ( ) l g π T () Procedure The radius of the bob is measured using vernier calipers. The length of the pendulum is equal to the distance from the point of suspension to the top of the bob plus the radius of the bob. The length is initially adjusted to be 0. m. The time (t) for 0 oscillations is determined twice using a stop clock and mean value of t is calculated. The period T is calculated as T t. The value of l is 0 T determined. The experiment is repeated for l 0.6 m, 0.7 m, 0.8 m, 0.9 m, m and. m. The l mean value of is calculated. The acceleration due to gravity (g) is calculated using equation (). T (l, T ) graph A graph is plotted with l along X-axis and T along Y-axis. This graph is called (l, T ) graph. It can be seen that (l, T ) graph is a straight line and can be used to calculated the length corresponding to any period. For a seconds pendulum, T seconds and hence, T. The length corresponding to T gives the length of the seconds pendulum. 7
Result Acceleration due to gravity at the place m/s Length of the seconds pendulum m Observations and Calculations Radius of the bob (r) Trial Legth of the No pendulum (l) m 0. 0.6 0.7 0.8 0.8 6.0 7. Time for 0 oscillations (s) (s) Mean (s) T (s) T (s ) l/t (m/s ) Mean value of (L/T ) m/s ( ) l Acceleration due to gravity g π T m/s From (l, T ) graph, length of the seconds pendulum m 8
Moment Bar Exp. No: Date: Aim (i) To nd the mass of the moment bar (ii) To nd the mass of the given body Apparatus Moment bar, weight hanger, slotted weights and unknown mass Principle Moment bar is a uniform bar like a meter scale. When the moment bar is in equilibrium under the action of coplanar parallel forces, then according to principle of moments, the sum of anticlockwise moments about any point equal to the sum of clockwise moments about the same point. The moment of a force about a given point is the product of the force and the perpendicular distance between the point and the line of action of the force. Procedure The centre of gravity (G) of the moment bar is determined rst. The moment bar will remain horizontal when supported at the centre of gravity. The position of G is noted by balancing the moment bar properly. To nd the mass of the moment bar The moment bar is suspended at a point O on one side of the centre of gravity G as shown in Fig.. The weight of the moment bar acts vertically downwards through the point G. A known weight W is suspended from a point A on the bar and the position of W is adjusted until the moment bar remains horizontal. Then according to the principle of moments, M GO W OA M W OA GO Here M is the mass of the moment bar. The experiment is repeated by changing the value of W and the average value of M is calculated. To nd the mass of the given body The moment bar is suspended at the centre of gravity G and the given body is suspended from a point B on one side of G as shown in Fig.. A known weight W is suspended on the other side of G and the position of W is adjusted until the moment bar remains horizontal. Then according to the principle of moments, m BG W AG 9
m W AG BG Here m is the mass of the given body. The experiment is repeated by changing the value of W and the average value of m is calculated. Result Mass of the moment bar Mass of the given body kg kg Observations and Calculations Position of the centre of gravity of the moment bar (G) (i) To nd the mass of the moment bar Trial No Known mass W Distance (gm) GO () 0 0 00 0 0 0 00 0 0 0 Distance OA () M W OA GO (gm) Mass of the moment bar gm 0 kg 0
(ii) To nd the mass of the given body Trial No Known mass W Distance (gm) BG () 0 0 00 0 0 0 00 0 0 0 Distance AG () M W AG BG (gm) Mass of the given body gm 0 kg
Convex Lens Exp. No: Date: Aim (i) To determine the focal length of the given convex lens by distant object method (ii) To determine the focal length of the given convex lens by u-v method (iii) To determine the focal length of the given convex lens from (u, v) graph Apparatus Convex lens, stand for mounting the lens, illuminated wire gauze, white screen and meter scale Principle A convex lens is an optical device which converges a parallel beam of light to a point by means of refraction. The point at which the light beam is converged is called the focus of the convex lens. The distance between the focus and optic centre of the convex lens is called its focal length (f). The distance between the lens and the object is called object distance (u) and the distance between the lens and the image is called image distance (v). The focal length of the convex lens is related to object distance and image distance by the equation, u + v f f uv (u + v) Procedure Distant object method The approximate focal length of the given convex lens is determined rst by distant object method. For this, the convex lens is mounted vertically on a stand and is placed in such a way as to face a very distant object. The screen is placed on the other side of the lens and its position is adjusted to get a well dened sharp image of the object. The distance between the lens and the screen is measured using a meter scale. This distance gives the approximate focal length of the lens since the image of a distant object will formed close to the focus of the lens. The experiment is repeated times and the mean value of the focal length is calculated. u-v method The given convex lens mounted vertically on a stand is directed towards the illuminated wire gauze which acts as the object (Fig.). The lens is initially placed at a distance slightly greater than the approximate focal length obtained by distant object method. The position of the screen is adjusted to get a clear image on it. The distance between the lens and the image is measured using a meter scale. The focal length of the convex lens is calculated using the formula,
f uv (u + v) The experiment is repeated for both magnied and diminished images. The average value of the focal length is then calculated. (u, v) graph A graph is plotted with u along X-axis and and v along Y-axis using the same scale factor for both u and v. The bisector of the angle XOY is drawn to meet the (u, v) graph at a point C as shown in Fig.. From the point C on the graph, perpendiculars CA and CB are drawn to the axes. Then, Hence, OA OB f f (OA + OB) Result (i) Focal length of the given convex lens by distant object method (ii) Focal length of the given convex lens by u-v method (iii) Focal length of the given convex lens from (u, v) graph Observations and Calculations Distant object method Distance between the lens and image of the distant object () () () Mean () u-v method Trial No u () v () f uv (u+v) () Mean f ()
From (u, v) graph Distance OA Distance OB Focal length, f (OA + OB)
Appendix. Vernier calipers. Screw Gauge. Simple pendulum