Class 11 Physics practical reading To find the weight of a given body using parallelogram law of vectors.

Aim

To find the weight of a given body using parallelogram law of vectors.

Apparatus Required

Gravesand's apparatus (a vertical wooden board with two pulleys), three hangers, a given body whose mass is to be determined, thin (but strong) string, white paper sheets, a mirror strip, thumb pins, protactor, half metre scale, a spring balance, etc.

Theory

Gravesand Apparatus

According to parallelogram law of vector addition, if two vectors can be represented in magnitude and direction by the adjacent sides of a parallelogram, then the resultant is represented by the diagonal of the parallelogram, in both magnitude and direction.

In Fig, if P and Q are the magnitudes of the two vectors and ϴ the angle between them, then the resultant R is given by
      R² = S² = P² + Q² + 2PQCosθ
where S is the vector having the same magnitude as the vector R but opposite direction.

Procedure

1. Place the Gravesand's appartus vertically and firmly on a table. Ensure the pulleys are moving smoothly.
2. Fix a white paper on the board, between the pulleys, using thumb pins.
3. Place a string over the pulley and at the two ends tie hooks of the hanger weights. Take another string and tie it in the middle of the string passing over the pulleys and suspend the unknown weight from this string.
4. Add and adjust slotted weight to the hangers, till the knot (of the two strings) lies at the centre of the sheet. 5. To mark the direction of forces place the plane mirror strip under each string in turn and mark the ends of the mirror strip by placing your eye in such a position that the image of string is covered by the string itself.
6. Remove the paper and join each pair of points and produce them to meet at O
7. Choose a convenient scale and mark the sides OA and OB (eg. if P = 200 gm wt. and Q = 150 gm wt). Mark OA = 4 unit and OB = 3 unit. Complete the parallelogram OACB. Join the diagonal OC and measure it and convert it into equivalent gm wt. in accordance with the chosen scale. This will be equal to the weight suspended at S. Also, measure the weight using spring balance for confirmation.
8. Repeat the experiment two more times by changing the weight in hangers P and Q.

Observations

Precautions

1. Ensure that the pulleys are frictionless.
2. The board should be stable and perfactly vertical.
3. The hangers should not touch the board.
4. The knot (or the point O) should be in the middle of the white paper sheet.
5. Marking should be done carefully with a sharp pencil.

Sources of Error

1. The board is not perfectly vertical. 2. The pulleys are not frictionless.
3. Error in marking the points.