Question

A string of length $l$ is fixed at one end and carries a mass $M$ at the other end. The string makes $\frac{2}{\pi}$ 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. $Ml$

Answer 1

Answer: (A)

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
$F=M r \omega^{2}$

In this case, $r=l \sin \theta$
$\therefore T \sin \theta=M l \sin \theta \omega^{2}$
$\Rightarrow T=M l \omega^{2}=M l(2 \pi f)^{2}$
$\Rightarrow T=M l\left(2 \pi \times \frac{2}{\pi}\right)^{2}$
$\Rightarrow T=16\, Ml$