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. A solid cylinder of mass m 4kg and radius
R-10cm has two ropes wrapped around it, one
near each end. The cylinder is held horizontally
by fixing the two free ends of the cords to the
hooks on the ceiling such that both the cords
are exactly vertical. The cylinder is released
to fall under gravity. Find the tension along
the strings.
1) 6.53N 2) 5.23N 3) 3.23N 4) 4.43N

Asked by chandanbr6004 25th November 2017, 2:20 PM
Answered by Expert
Let a be the acceleration when the cylinder is falling freely.
m × a =  m × g - 2×T  ............................(1)
Let r be the radius of cylinder. If torque acting on both the ends are similar then net torque is given by
begin mathsize 12px style tau space equals space tau subscript 1 plus tau subscript 2 space equals space 2 cross times r cross times T space equals space I cross times alpha end style ...........................(2)
Where I is moment of inertai and α is angular acceleration due to rod rotation.
if we substitute for I and α in the above equation we get 
begin mathsize 12px style 2 cross times r cross times T space equals space 1 half m r squared open parentheses a over r close parentheses space equals space 1 half m cross times r cross times a

H e n c e space T space equals space 1 fourth m cross times a end style
Substituting the above equation for T in eqn.(1) , we get  a = (2/3)g 
Hence T = (1/4)×4×(2/3)x9.8 = 6.53 N
Answered by Expert 29th November 2017, 3:46 PM
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