A string of length ' ell ' fixed at one end c | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The frequency of revolution is $f = \frac{3}{\pi} 	ext{ rev/s}$.The angular velocity is $\omega = 2\pi f = 2\pi \left( \frac{3}{\pi} ight) = 6

Vedclass · Accepted Answer

$36 m \ell$

Vedclass · Answer

(B) The frequency of revolution is $f = \frac{3}{\pi} 	ext{ rev/s}$.The angular velocity is $\omega = 2\pi f = 2\pi \left( \frac{3}{\pi} ight) = 6 	ext{ rad/s}$.For a conical pendulum,the tension $T$ in the string is given by the centripetal force equation $T \sin 	heta = m \omega^2 r$ and the vertical balance $T \cos 	heta = mg$.However,in the limit where the angle $	heta$ is small,or considering the radial component of tension providing the centripetal force,we have $T = m \omega^2 \ell$ if we assume the string is horizontal,but generally $T \cos 	heta = mg$ and $T \sin 	heta = m \omega^2 (\ell \sin 	heta)$.Thus,$T = m \omega^2 \ell$.Substituting the values: $T = m (6)^2 \ell = 36 m \ell$.

$A$ string of length ' $\ell$ ' fixed at one end carries a mass 'm' at the other end. The string makes $\frac{3}{\pi}$ revolutions per second around the vertical axis through the fixed end as shown in the figure. The tension '$T$' in the string is:

Similar Questions

$A$ string of length $0.1\,m$ cannot bear a tension more than $100\,N$. It is tied to a body of mass $100\,g$ and rotated in a horizontal circle. The maximum angular velocity can be .......... $rad/s$.

$A$ small disc is placed on the top of a smooth hemisphere of radius $R$. What is the smallest horizontal velocity $v$ that should be given to the disc for it to leave the hemisphere immediately at the top and not slide down it? [There is no friction]

$A$ uniform chain of mass $m$ and length $L$ is originally placed mid-way on the top of a fixed smooth double-sided wedge. The length of each side of the wedge is $L$. It is then given a slight push. The kinetic energy of the chain when the whole chain has just slid to the left side of the wedge is:

$A$ person with his hand in his pocket is skating on ice at the rate of $10 \ m/s$ and describes a circle of radius $50 \ m$. What is his inclination to the vertical? (Take $g = 10 \ m/s^2$)

If the radii of circular paths of two particles of same mass are in the ratio of $1: 2$, then to have a constant centripetal force, the ratio of their speeds should be

Vedclass Test Series

Exam Paper Generator

Online Exam Module