A string just breaks under a load of 50 kg. | vedclass

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

Question

(B) The maximum tension the string can withstand is $T_{\max} = mg = 50 	imes 10 = 500 \ N$.For a mass $m$ rotating in a horizontal circle of radius

Vedclass · Accepted Answer

$\frac{\sqrt{50}}{2 \pi} 	ext{ rps}$

Vedclass · Answer

(B) The maximum tension the string can withstand is $T_{\max} = mg = 50 	imes 10 = 500 \ N$.For a mass $m$ rotating in a horizontal circle of radius $r$ with angular velocity $\omega$,the tension $T$ is given by $T = m \omega^2 r$.In this case,the length of the string $L = 10 \ m$ acts as the radius $r$ (assuming the string remains horizontal for the maximum speed case).Substituting $\omega = 2 \pi n$,where $n$ is the frequency in revolutions per second (rps):$T_{\max} = m (2 \pi n_{\max})^2 L$$500 = 1 	imes (2 \pi n_{\max})^2 	imes 10$$50 = (2 \pi n_{\max})^2$$2 \pi n_{\max} = \sqrt{50}$$n_{\max} = \frac{\sqrt{50}}{2 \pi} 	ext{ rps}$.

$A$ string just breaks under a load of $50 \ kg$. $A$ mass of $1 \ kg$ is attached to one end of this string $10 \ m$ long and is rotated in a horizontal circle. Calculate the greatest number of revolutions that the mass can make in one second without breaking the string. (Take $g = 10 \ m/s^2$)

Similar Questions

$A$ circular road of radius $1000 \, m$ has a banking angle of $45^\circ$. The maximum safe speed of a car having mass $2000 \, kg$ will be,if the coefficient of friction between the tyre and road is $0.5$,equal to ....... $m/s$.

$A$ gramophone record is rotating with an angular velocity $\omega$. $A$ coin is placed at a distance $r$ from the center of the record. The coefficient of static friction is $\mu$. The coin will revolve with the record if .......

$A$ person is driving a vehicle at a uniform speed of $5 \text{ ms}^{-1}$ on a level curved track of radius $5 \text{ m}$. The coefficient of static friction between the tyres and the road is $0.1$. Will the person slip while taking the turn with the same speed? (Take $g = 10 \text{ ms}^{-2}$)

$A$ car moves along a circular track of radius $R$ banked at an angle of $30^o$ to the horizontal. The coefficient of static friction between the wheels and the track is $\mu$. The maximum speed with which the car can move without skidding out is

$A$ man is standing on a rough $(\mu = 0.5)$ horizontal disc rotating with a constant angular velocity of $5 \ rad/s$. At what distance from the center should he stand so that he does not slip on the disc?

Vedclass Test Series

Exam Paper Generator

Online Exam Module