$A$ string of length $L$ fixed at one end carries a body of mass $m$ at the other end. The mass is revolved in a circle in the horizontal plane about a vertical axis passing through the fixed end of the string. The string makes an angle $\theta$ with the vertical. The angular frequency of the body is $\omega$. The tension in the string is

  • A
    $mL^2 \omega$
  • B
    $mL \omega^2$
  • C
    $\frac{\omega^2}{mL}$
  • D
    $\frac{m \omega^2}{L}$

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Similar Questions

One end of a string of length $l$ is connected to a particle of mass $m$ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$,the net force on the particle (directed towards the centre) is :
$(i) \; T$
$(ii) \; T - \frac{m v^{2}}{l}$
$(iii) \; T + \frac{m v^{2}}{l}$
$(iv) \; 0$
$T$ is the tension in the string. [Choose the correct alternative].

$A$ rod $(AB)$ is attached to a fixed point $(C)$ using a light rope $(AC)$. The other end of the rod $(B)$ is resting on ice with negligible friction,and the system is in a stationary position. Which of the following can be the equilibrium configuration of this system?

$A$ person with his hands in his pockets is skating on ice at a velocity of $10 \, m/s$ and describes a circle of radius $50 \, m$. What is his inclination with the vertical?

$A$ cyclist riding a bicycle at a speed of $14\sqrt{3} \text{ m/s}$ takes a turn around a circular road of radius $20\sqrt{3} \text{ m}$ without skidding. Given $g = 9.8 \text{ m/s}^2$,what is his inclination to the vertical in degrees?

Consider the following statements:
Assertion $(A)$: $A$ cyclist always bends inwards while negotiating a curve.
Reason $(R)$: By bending,he provides the necessary centripetal force by shifting his centre of gravity.

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