Question

A uniform rope is rotated along horizontal plane about vertical axis passing through the one end with uniform angular velocity $\omega$ . If $T$ is the tension in the rope at a distance $x$ from the axis of rotation, then:
1) $T\propto {\omega }^2$
2) $T\propto \omega$
3) $T\propto x^2$
4) $T\propto x$

• A. 1 and 3 are true
• B. 1 and 4 are true
• C. 2 and 3 are true
• D. 3 and 4 are true

Answer 1

The correct option is B 1 and 4 are true

Acceleration of a particle which is at a distance x from the axis of rotation is ${\omega }^{2}x$ and this is provided by the Tension, thus$T\propto {\omega }^{2}andT\propto x$