A disc revolves with a speed of 33 frac{1}{3} | vedclass

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

Question

(B) For a coin to revolve with the disc,the frictional force must be greater than or equal to the required centripetal force: $\mu mg \geq mr\omega^2$

Vedclass · Accepted Answer

Only the coin at $4 \; cm$

Vedclass · Answer

(B) For a coin to revolve with the disc,the frictional force must be greater than or equal to the required centripetal force: $\mu mg \geq mr\omega^2$,or $\mu g \geq r\omega^2$.Given:Frequency $
u = 33 \frac{1}{3} \; rev/min = \frac{100}{3 	imes 60} = \frac{5}{9} \; rev/s$.Angular velocity $\omega = 2\pi
u = 2 	imes \pi 	imes \frac{5}{9} = \frac{10\pi}{9} \approx 3.49 \; rad/s$.Maximum acceleration provided by friction $a_{max} = \mu g = 0.15 	imes 10 = 1.5 \; m/s^2$.For the coin at $r_1 = 4 \; cm = 0.04 \; m$:Required centripetal acceleration $a_1 = r_1\omega^2 = 0.04 	imes (3.49)^2 \approx 0.49 \; m/s^2$.Since $a_1 For the coin at $r_2 = 14 \; cm = 0.14 \; m$:Required centripetal acceleration $a_2 = r_2\omega^2 = 0.14 	imes (3.49)^2 \approx 1.70 \; m/s^2$.Since $a_2 > a_{max}$ $(1.70 > 1.5)$,the coin at $14 \; cm$ will slip.

Similar Questions

The maximum velocity (in $m/s$) with which a car driver must traverse a flat curve of radius $150\, m$ and coefficient of friction $0.6$ to avoid skidding is ........ $m/s$.

$A$ block $(P)$ is rotating in contact with the vertical wall of a rotor as shown in figures $A$,$B$,and $C$. Find the relation between angular velocities $\omega_A, \omega_B$,and $\omega_C$ such that the block does not slide down. ($R_A < R_B < R_C$ are the radii).

$A$ car of mass $m$ moves on a banked road having radius $r$ and banking angle $\theta$. To avoid slipping from the banked road,the maximum permissible speed of the car is $v_0$. The coefficient of friction $\mu$ between the wheels of the car and the banked road is:

$A$ car is negotiating a curved road of radius $R$. The road is banked at an angle $\theta$. The coefficient of friction between the tyres of the car and the road is $\mu_s$. The maximum safe velocity on this road is

An unbanked curve has a radius of $60\,m$. The maximum speed at which a car can make a turn if the coefficient of static friction is $0.75$,is ........ $m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module