Find the radius of the pulley if a rotation of 51.6 degrees raises the weight 11.4 cm
The length of the arc measuring 51.6 degrees is 11.4 cm.
Use proportions to convert 51.6 degrees to radians:
where x is the value of 51.6 degrees in radians. Solve for x:
The arc length is equal to the angle in radians multiplied by the radius of the circle:
Solve for r and substitute 11.4 cm for arc length and 0.9 for theta.
Therefore the radius of the pulley is equal to 12.7 cm.
Unitary method to find circumference of pulley
51.6 degree gives a lift of 11.4 cm
so 1degree gives a lift of (11.4/51.6) cm
so 360 degree gives a lift of (11.4/51.6)*360 =circumfrence of pulley
Formula for circumfrence of circle is C = 2πr
therefore (11.4/51.6)*360 = 2 *3.14 *radius of pulley
radius of pulley = (11.4*360)/(51.6*2*3.14) cm = 12.66 cm
Ans- The radius of pulley is 12.66 cm :)