A string of length l is fixed at one end and carries a mass M at the other end. The string makes (2/π) rev/s around the vertical axis through the fixed end as shown in the figure, the tension in the string is :

Question

A string of length l is fixed at one end and carries a mass M at the other end. The string makes (2/π) rev/s around the vertical axis through the fixed end as shown in the figure, the tension in the string is : (A) 16 Ml (B) 4 Ml (C) 2 Ml (D) Ml

Tardigrade Admin · Accepted Answer

Outward force acting on the mass is known as centrifugal force.
An object travelling in a circle behaves as if it is experiencing an outward force. This force is known as centrifugal force, which actually does not exist and is given by

F = M r ω^{2}

In this case,

r = l sin θ

∴ T sin θ = Ml sin θ ω^{2}

\Rightarrow T = Ml ω^{2} = Ml (2 π f)^{2}

\Rightarrow T = Ml (2 π \times \frac{2}{π})^{2}

\Rightarrow T = 16 Ml

Q. A string of length $l$ is fixed at one end and carries a mass $M$ at the other end. The string makes $\frac{2}{π}$ rev/s around the vertical axis through the fixed end as shown in the figure, the tension in the string is :

$16 Ml$

$4 Ml$

$2 Ml$

$Ml$

Q. A string of length l is fixed at one end and carries a mass M at the other end. The string makes π2​ rev/s around the vertical axis through the fixed end as shown in the figure, the tension in the string is :

16Ml

4Ml

2Ml

Ml

Q. A string of length $l$ is fixed at one end and carries a mass $M$ at the other end. The string makes $\frac{2}{π}$ rev/s around the vertical axis through the fixed end as shown in the figure, the tension in the string is :

$16 Ml$

$4 Ml$

$2 Ml$

$Ml$