A block of mass 0.4 kg is attached to a vertical rotating spindle by two strings of equal length of 1m as in figure. The period of rotation is 0.4 π sec . Then the value of 2 T 1 /5 is (in N)

Question

A block of mass 0.4 kg is attached to a vertical rotating spindle by two strings of equal length of 1m as in figure. The period of rotation is 0.4 π sec . Then the value of 2 T 1 ​ /5 is (in N)

TestHub · Accepted Answer

Geometry: r = 1 2 − 0. 8 2 ​ = 0.6 m, cos θ = 0.8 , and ω = 0.4 π 2 π ​ = 5 rad/s. Vertical: ( T 1 ​ − T 2 ​ ) ( 0.8 ) = m g = 4 ; radial: ( T 1 ​ + T 2 ​ ) ( 0.6 ) = m ω 2 r = 6 . Solving, T 1 ​ = 7.5 N, so 5 2 T 1 ​ ​ = 3 .

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