Physics Practicals Class XI
Determining the weight of a given body using the parallelogram law of vectors.
The objective of the Experiment :
Our objective is to find the weight of a given body using the Parallelogram Law of Vectors.
Theory
What does the Parallelogram Law of Vectors state?
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If two vectors acting simultaneously on a particle are represented in magnitude and direction by the two adjacent sides of a parallelogram drawn from a point, then their resultant is completely represented in magnitude and direction by the diagonal of that parallelogram drawn from that point.
Parallelogram Law of Vectors explained
Let two vectors P and Q act simultaneously on a particle O at an angle 
. They are represented in magnitude and direction by the adjacent sides OA and OB of a parallelogram OACB drawn from a point O.Then the diagonal OC passing through O, will represent the resultant R in magnitude and direction.
On a Gravesand's apparatus, if the body of unknown weight (say S) is suspended from the middle hanger and balancing weights P and Q are suspended from othe two hangers then,
or
The unknown weight can be calculated from the equation (1).
On a Gravesand's apparatus, if the body of unknown weight (say S) is suspended from the middle hanger and balancing weights
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P and Q are suspended from the other two hangers then,
Now construct a parallelogram OACB by assuming a scale (say 1cm=50 gwt) corresponding to the weights P and Q. The diagonal of the parallelogram OC will give the resultant vector. The weight of the unknown body,
If W is the actual weight of the body, then the percentage error in the experiment can be calculated using the equation,
Learning Outcomes
- Students learn what is parallelogram law of vectors.
- They become familiar with the Gravesands apparatus.
- Students are able to find the unknown weight of an object using the parallelogram law of vectors.
Materials Required :
- Parallelogram Law of Forces apparatus (Gravesand's apparatus)
- Plumb line
- Two hangers with slotted weights
- A body (a wooden block) whose weight is to be determined
- Thin strong thread
- White drawing paper sheet
- Drawing pins
- Mirror strip
- Sharp pencil
- Half meter scale
- Set squares
- Protractor
Lab Procedure :
- Set up the Gravesand's apparatus and ensure its board is vertical. This can be tested using the plumb line. Test if the pulleys (let us name them - P1 and Q1) are frictionless. If you feel any friction, oil them.
- Fix the white drawing paper sheet to the board using the drawing pins.
- Take three pieces of strong threads and tie one end of all three together to make a knot. (Let us name this knotted end - O). This knot becomes the junction of the three threads.
- From the other ends of the two threads, tie a weight hanger with the same slotted weights in each; we will name these weights as P and Q.
- From the end of third thread tie the given body, which is the wooden block, which we will name as S.
- Pass the threads with weights P and Q over the pulleys and let the third thread with the block S, stay vertical in the middle of the board.
- The weights P, Q and the wooden block S acts as the three forces along the three threads. At the junction O, the forces are in equilibrium.
- Now adjust the weights P and Q (forces) such that the junction O stays in equilibrium slightly below the middle of the paper.
- See that all the weights hang freely and that none of them touch the board or the table.
- Mark the position of junction O on the paper using a sharp pencil.
- Slightly disturb the weights P and Q and then leave them.
- Once settled, note the position of junction O. Make sure that this point is very close to the earlier position.
- Take the mirror strip and keeping it lengthwise under each thread, mark the position of the ends of the image of the thread in the mirror, covering the image by the thread. These new positions are P1, P2 for the thread with the weight P, and Q1 and Q2 for the thread with the weight Q and S1, S2 for the thread with the weight S.
- Remove the paper from the board and with the help of the half metre scale draw lines through the points P1 and P2 to represent P, through points Q1 and Q2 to represent Q and through points S1 and S2 to represent S. These lines must meet at point O.
- Assuming a scale of 1cm = 50 g, mark OA = 3 cm and OB =3 cm to represent P=150g and Q= 150g.
- Complete parallelogram OACB using the set squares and join OC. This represents the resultant vector R which corresponds to the weight S.
- Measure OC and multiply it by the scale (50 g) to get the value of the unknown weight (S).
- For different sets of observation, change P and Q suitably.
- We can find the weight of the wooden block (R) using the equation (1).
- Take the mean of the two values to get the actual weight of the body.
- To find the percentage error in the experiment, measure the actual weight of the body using a spring balance.
- Calculate the percentage error using equation (3).
Observations
To find the actual weight of the unknown mass, W
Least count of spring balance = _________g
Zero error of spring balance = ________g
Weight of unknown body by spring balance = ________g
To find the weight of the unknown mass using parallelogram law of vectors
Scale. Let 50 g=1 cm
| No:of obs | Forces | Valuesof | Slides | Resultant force R (g wt) | Unknown weight S (g wt) | Weight by spring balance (g wt) | Error (g wt) |
||||
| P (g wt) | Q (g wt) |  |
cos |
OA (cm) | OB (cm) | OC (cm) | |||||
| 1 | |||||||||||
| 2 | |||||||||||
| 3 | |||||||||||
| 4 | |||||||||||
| 5 | |||||||||||
Calculation
Mean value of unknown weight S = ---------- gwt.
Mean value of unknown weight, R =---------gwt
Unknown weight = (S+R)/2 = ------------gwt= ---------------kgwt
Percentage error = ---------
Result
The unknown weight of given body = ------------------ kgwt .
The result shows the error is within limits of the experiment error.
Precautions
- 1. The board should be stable and ver
- 2. The pulleys should be friction
- 3. The hangers should not touch the board or
- 4. Junction O should be in the middle of the paper
- 5. Points should be marked only when weights are at r
- 6. Points should be marked with sharp
- 7. Arrows should be marked to show direction of for
- 8. A proper scale should be taken to make fairly big parallelogr
Sources of error :
- 1. Pulleys may have
- 2. Weights may not be accurate
- 3. Points may not be marked correctly.
- 4. Weight measured by spring balance may not be much accurate
Viva-Voce [Parallelogram Law of Vectors]
Q.1: What are scalar and vector quantities?
Ans. (a) Scalar is a physical quantity which is completely represented only by magnitude with a suitable unit, having no direction, e.g. time, mass, speed, density, work, energy, etc.
(b) Vector is a physical quantity has both ‘magnitude and a specified direction’ e.g. displacement, velocity, acceleration, force, weight, torque, momentum, magnetic field intensity, electric field intensity.
Q.2: Define resolution of vectors?
Ans. The splitting up of a single vector into two or more vectors is called resolution of vector.
Q.3: What do you mean by components of a vector?
Ans. Two or more such vectors which are at right angle to each other are called rectangular components.
Q.4: What are rectangular component?
Ans. The components of a vector which are at right angle to each other are called rectangular components.
Q.5: Define the following: (a) unit vector (b) null vector (c) position vector (d) negative vector
Ans. (a) Unit vector is that vector whose magnitude is unity ‘1’, and it simply indicates the direction.
(b) Null vector is that vector whose magnitude is zero and it may have any arbitrary direction or no direction. It is also called zero vector.
(c) Position vector is that vector which specifies the position of a point with respect to origin of reference axes.
(d) The negative of a vector is that vector which is equal in magnitude but opposite in direction of that vector.
Q.6: State head to tail rule of addition of vectors?
Ans. It states that ‘When the representative lines of all the given are drawn, arrange them in such a way that head of first vector line joins with the tail of second vector, then head of second vector joins with the tail of third vector and so on. The line joining the tail of first vector with head of last vector will represent the resultant vector in magnitude and direction’.
Q.7: State parallelogram law of vector addition?
Ans. It states that ‘If two vectors are completely represented by two adjacent sides of a parallelogram, then the diagonal of the parallelogram from the tails of two vectors gives their resultant vector’.
Q.8: What is a scalar product?
Ans. When the product of two vectors is a scalar quantity it is called scalar product or dot product, e.g. work is a dot product of force and displacement.
Q.9: What is a vector product?
Ans. When the product of two vectors is a vector quantity it is called vector product or cross product, e.g. torque is a vector product of force and force arm.
Q.10: How a vector is multiply by a number?
Ans. When a vector is multiplied by a positive number its magnitude changes but direction remains the same. But when a vector is multiplied by a negative number not only its magnitude changes but its direction is also reversed.
Question. 11. Can the law of vectors be used to add forces and velocities ?
Answer. Yes, they can be used, because forces and velocities are also vectors.
Question. 12. Why is addition of vectors different from addition of scalars ?
Answer. Because vectors have direction also, which makes all the difference
Question. 13. Why is addition of vectors called composition of vectors ?
Answer. Composition means collection. By addition we collect (convert) many vectors into one single vector.
Question. 14. What is meant by resolution of vectors ?
Answer. It is reverse of composition of vectors. The breaking of a single vector into its components is called resolution of vectors.
Question. 15. What are rectangular components ?
Answer. The two components of a vector, which are perpendicular to each other, are called rectangular (or right angular) components.
Question. 16. What are the main sources of error in the experiment using Gravesand’s apparatus ?
Answer. Its sources of error are
(1) Friction in the pulleys. (2) Weights in the threads.
Question. 17. Why the thread junction does not come at rest at same position always ?
Answer. It is due to friction on the pulleys.
Question. 18. How can this friction be reduced ?
Answer. It is done by oiling the pulleys.
Question. 19. Why the suspended weights are kept free from board or table ?
Answer. So that their effective weight may not become different due to reaction of board or table.
Question 20.: What is the unit of force?
Ans. The force is measured in Newton (MKS system) or in dyne (CGS system) or in pound (BE system).
Physics is one of the most important subjects in Class 12. As the CBSE exam approaches, students get busy preparing for different subjects. But an essential part of the CBSE exam is the practical exams which consist of 30 marks.
Students must know all the experiments along with theorems, laws, and numerical to understand all the concepts of 12th standard physics in a detailed way. Two experiments (8 + 8 marks) are asked from each section in the practical exam. The experiment records and activities consist of 6 marks, the project has 3 marks and viva on the experiment consist of 5 marks.
The Physics Practicals For Class 12 CBSE is given here so that students can understand the experiments in a better way. Students are suggested to study the theory and law behind the experiment properly before performing the experiment.Also Go through the viva voce questions and answers for each and every experiment which are provided on the website .