A string of length L is fixed at one end and carries a mass of M at the other end. The mass makes rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is __________ ML. [2025]

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Solution

Q.

A string of length L is fixed at one end and carries a mass of M at the other end. The mass makes $(\frac{3}{π})$ rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is __________ ML. [2025]

Ans.
(36)

T cos $θ$ = mg ... (i)

T sin $θ$ = M $ω^{2}$ R ... (ii)

Using equation (ii)

T sin $θ$ = M $ω^{2}$ (L sin $θ$ )

$T = M ω^{2} L = M {(\frac{3}{π} \times 2 π)}^{2} L = 36 M L$

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