To Verify Laws Of Moments Graphically And Analyze The Relation Between Clockwise VS. Anticlockwise Moment Using Meters Scale Suspended At Its Center By An Inter Extensible String

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APPARATUS REQUIRED

i) A meter scale

ii) Slotted weight

iii) Stand

iv) String

v) Unknown body

THEORY:

Principle of moment:

It states that when a body in equilibrium is under the action of numbers of forces, then the moment of these forces about any point is zero. That is sum of clockwise moments. The principle may be utilized to find the magnitude and direction of an unknown force acting on a body in equilibrium. In the diagram if F₁ and F₂ be two forces acting at A and B of the right body is in equilibrium about the point 0. Then by principle of moment F₁ = OB = F₂x0A

If a unbrown weight ‘W’ is suspended at the end A of a meter scale and known weight ‘Wo’ be suspended at the end B as shown in fig, and then position of the point O(i.e. fulcrum) is so, adjusted than the meter scale is in equilibrium. From the principle of moments, we have.

W x OA = Wo xOB

          W= OB/OA x Wo

therefore, w= b/a xWo

OBSERVATION:

No.of obsWeight on the armOA          OB F₂ (gm)    F1(cm)Distance of CG from points (A and B)OA               OB(cm)              (cm)Clockwise momentOA x F2(gm.cm)Anticlockwise moment OB x Fi(gm.cm)Result
110           2020                 10200200
2100          5010.1              2010101000
3100          206.1                29.9610598
450             20.210                 25500512.5
5150           206                   45.6900912 

Table 2: For unknown weight.

No.of obs.Known weight Wo (gm)Unknown weight on right arm (w) OA    OB           unknown                       Weight (w)=                       OA/OB xWo                          gm(a)                  Unknown weight on left arm (w) OB    OA    unknown                  Weight (w)=                  OA/OB xWo                     gm(b)        Mean of (a)and(b)(gm)Final mean weight (gm)
1107          32.6       46.5728        6           46.6746.62
2209.2       21.4        46.5223.4     10          46.846.66
35020         18.7        46.7530        32.4        46.3046.5246.605
410032.5      15            46.154.7       10            4746.575
515050         15.6          46.86.2        20            46.546.65

The weight of the unknown body measured by the beam balance

 (W) = 46.89gm

RESULT

From this experiment we conclude that when a body is acted on by a number of forces under equilibrium the sum of the clockwise moment and the anticlockwise moment about a point are equal. Also the weight of an unknown body is found to be 46.605gm.

Sources of errors

1. The thread tied to the meter rod may not be exactly at the CG of it.

2. The meter rod may not exactly be at equilibrium due to external causes like fan, wind, etc.

3. At the point of equilibrium, the meter rod may not be exactly horizontal.

4. Error may be due to carelessness of the experiment.

PRECAUTIONS:

1. The C.G. of the meter red should be carefully marked. The meter rod must be allowed to rest on a sharp edge exactly at its C.G.

2. The weight should be suspended away from C.G.

3. In the position of equilibrium, the meter rod should be horizontal.

4. The thread should be tied exactly at the C.G. of the meter rod

5. Experiments should be performed carefully.

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