A mass of 0.5 kg is attached to a string mov | vedclass

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

Question

(A) The tension $T$ in a string for a mass $m$ moving in a horizontal circle of radius $r$ with angular velocity $\omega$ is given by the centripetal

Vedclass · Accepted Answer

$\frac{1}{3} \ cycle/s$

Vedclass · Answer

(A) The tension $T$ in a string for a mass $m$ moving in a horizontal circle of radius $r$ with angular velocity $\omega$ is given by the centripetal force: $T = m r \omega^2$.Since $m$ and $r$ are constant,we have $T \propto \omega^2$.Let the initial angular velocity be $\omega_1 = 10 \ cycle/min = \frac{10}{60} \ cycle/s = \frac{1}{6} \ cycle/s$.Let the initial tension be $T_1$ and the final tension be $T_2 = 4T_1$.Using the proportionality $T \propto \omega^2$,we get $\frac{T_2}{T_1} = \left( \frac{\omega_2}{\omega_1} ight)^2$.Substituting the values: $4 = \left( \frac{\omega_2}{\omega_1} ight)^2$,which implies $\frac{\omega_2}{\omega_1} = 2$.Therefore,$\omega_2 = 2 \omega_1 = 2 	imes \frac{1}{6} \ cycle/s = \frac{1}{3} \ cycle/s$.

$A$ mass of $0.5 \ kg$ is attached to a string moving in a horizontal circle with an angular velocity of $10 \ cycle/min$. Keeping the radius constant,the tension in the string is made $4$ times by increasing the angular velocity to $\omega$. The value of $\omega$ for that mass will be:

Similar Questions

$A$ single wire $ACB$ passes through a smooth ring at $C$ which revolves at a constant speed in a horizontal circle of radius $r$ as shown in the figure. The speed of revolution is

$A$ particle is moving with constant speed along a uniform helical path $(a)$ and a spiral path $(b)$ separately,as shown in the figure.

$A$ train is moving with a speed of $12 \,m/s$ on rails which are $1.5 \,m$ apart. To negotiate a curve of radius $400 \,m$, the height by which the outer rail should be raised with respect to the inner rail is (Given, $g = 10 \,m/s^2$): (in $\,cm$)

$A$ stone of mass $2 \,kg$ is tied at one end of a string of length $2 \,m$ and is whirled in a horizontal circle. If the string can withstand a maximum tension of $64 \,N$, then the permissible maximum number of rotations per minute is

$A$ $500\, kg$ crane takes a turn of radius $50\, m$ with a velocity of $36\, km/hr$. The centripetal force is ......... $N$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module