A large drum having radius R is spinning arou | vedclass

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

Question

(D) For the body of mass $M$ to remain stuck to the inner wall of the rotating drum, the normal force $N$ exerted by the wall provides the necessary c

Vedclass · Accepted Answer

$\sqrt{\frac{g}{\mu R}}$

Vedclass · Answer

(D) For the body of mass $M$ to remain stuck to the inner wall of the rotating drum, the normal force $N$ exerted by the wall provides the necessary centripetal force: $N = M \omega^2 R$ The frictional force $f$ acts vertically upwards to balance the gravitational force $Mg$ acting downwards: $f = Mg$ Since the body is on the verge of slipping, the frictional force is at its maximum value, given by $f = \mu N$: $Mg = \mu N$ Substituting the expression for $N$ into the friction equation: $Mg = \mu (M \omega^2 R)$ Dividing both sides by $M$ and solving for $\omega$: $g = \mu \omega^2 R$ $\omega^2 = \frac{g}{\mu R}$ $\omega = \sqrt{\frac{g}{\mu R}}$

Similar Questions

$A$ cyclist leans at an angle of $30^{\circ}$ with the vertical while negotiating a circular road of radius $20 \sqrt{3} \,m$. The speed of the cycle should be

$A$ train runs along an unbanked circular track of radius $30 \; m$ at a speed of $54 \; km/h$. The mass of the train is $10^{6} \; kg$. What provides the centripetal force required for this purpose - the engine or the rails? What is the angle of banking required to prevent wearing out of the rail?

$A$ car of $800 \,kg$ is taking a turn on a banked road of radius $300 \,m$ and angle of banking $30^{\circ}$. If the coefficient of static friction is $0.2$, then the maximum speed with which the car can negotiate the turn safely is: $(g=10 \,m/s^2, \sqrt{3}=1.73)$ (in $\,m/s$)

$A$ motorcycle is travelling on a curved track of radius $500\,m$. If the coefficient of friction between the road and tyres is $0.5$,the maximum speed to avoid skidding will be ....... $m/s$. (Take $g = 10\,m/s^2$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module