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Two metallic cylinders of same material and radii r and 2r are joined as shown in figure. If top end is fixed and lower end of cylinder B is twisted by angle θ, then would the torque on both the cylinders be same ???

Two metallic cylinders of same material and radii r and 2r are joined as shown in figure. If top end is fixed and lower end of cylinder B is twisted by angle θ, then would the torque on both the cylinders be same ???

Question Image
Grade:11

1 Answers

Arun
25763 Points
2 years ago
Dear Abhishek
 
Let the total angle twisted by A and B is (not mentioned in question) and twist angle made by A and B will be θ1 and θ2 respectively.
hence θ=θ1+θ2.......1>  (total angle twisted is contribution of individual angular twist)
now the force applied produce the torque on B and a restoring torque is produce in A to counter torque of B this continuous till  both the rods does not archives the condition of equilibrium.
using the formula of torque  in both cylinder A and B 
Torque clockwose by B = torque anticlockwise by A
n* pi* (2r)4  theta2/ 2L = n * pi* (r)4 theta1/ 2L
Theta1 = 16 * theta2
Hence
Theta2 + 16 theta2 = theta
Theta2 = theta/17
And
Theta1 = 16 theta/17

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