DETERMINATION OF MODULUS OF RIGIDITY OF A WIRE BY STATICAL METHOD USING HORIZONTAL PATTERN OF APPARATUS

  • Theory: The Modulus of Rigidity

η= \( 180MgD(L1-L2)/π^2r^4(θ1 – θ2 ) \)     …………….(1)

where     M = load suspended.

D = Diameter of the pulley.

R = Radius of the experimental rod.

G = Acceleration due to gravity.

L1 – L2 = distance between two pointers.

θ1 – θ2 = Difference of the angular twist produced in the rod. 

  • Apparatus used:
  • Horizontal pattern of apparatus.
  • Set of ½ kg weights.
  • Scale
  • Screw gauge.
  • Experimental Results:
  • Table for least count of the screw gauge:
Pitch of the screw(p)  (cm) No. of circular scale   division Least count = p/n           (cm)
     

                   Zero error of the screw gauge = …………. c.m. 

  • Table for determination of the radius (r) of the rod:
Sl

No

Reading along any direction (X) Reading along perpendicular to the previous direction (Y) Uncorrected  diameter (X+Y)/2

(cm)

Mean uncorrected diameter

(cm)

Mean corrected diameter

(cm)

Mean radius (r)

(cm)

msr

(cm)

csr total   (cm) msr

(cm)

csr total (cm)
                     
               
               
  • Table for the Determination of the diameter (D) of the pully:
Circumference of the pully (L) in cm Radius of the pully (R) in cm Diameter of the pully (D) in cm
     
  • Difference in the length between the two pointer (L1 – L2) = ……… cm

 

  • Table for the determination of the Twist:
No of obs Weight placed on the pan (M) in gm Twist of the first pointer in degree (θ1) Twist of the second pointer in degree (θ2) 12) in degree
Load increasing Load decreasing Mean value of angle of twist (θ1)  Load increasing Load decreasing Mean value of angle of twist (θ2)
1 0              
2 500              
3 1000              
             
  • Calculation:

 

  •  Percentage Error :

\( dη/η=dM/M+dg/g+dD/D+d(L1-L2)/(L1-L2)+4dr/r+d(θ1 – θ2 )/(θ1 – θ2 ) \)

\( dM \) =0, \( dg \) =0, \( dD \) =0.1cm, \( d(L1-L2) \) =2 *0.1 cm, dr=least count of  the screw gauge,

                      d(θ1 – θ2 )=2*10.

Percentage error = \( dη/η  \)  *100%

  • Result:  The modulus of  rigidity ( η) of the rod is ….. dyne/cm2

 

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