A solid cylinder of mass m is wrapped with an | vedclass

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

Question

(C) Let the solid cylinder be in equilibrium.The forces acting along the inclined plane are the tension $T$ and the friction $f$. The component of gra

Vedclass · Accepted Answer

$\frac{mg}{5}$

Vedclass · Answer

(C) Let the solid cylinder be in equilibrium.The forces acting along the inclined plane are the tension $T$ and the friction $f$. The component of gravity along the plane is $mg \sin 60^{\circ}$.For translational equilibrium: $T + f = mg \sin 60^{\circ} \quad ......(i)$For rotational equilibrium about the center of the cylinder: $TR - fR = 0 \implies T = f \quad ......(ii)$Substituting $(ii)$ into $(i)$: $2f = mg \sin 60^{\circ} \implies f = \frac{mg \sin 60^{\circ}}{2} = \frac{mg \sqrt{3}}{4} \approx 0.433 mg$.The limiting friction is $f_{L} = \mu_{s} N = \mu_{s} mg \cos 60^{\circ} = 0.4 	imes mg 	imes 0.5 = 0.2 mg$.Since the required friction $(0.433 mg)$ is greater than the limiting friction $(0.2 mg)$,the cylinder will not remain in static equilibrium and will roll down.The friction acting will be kinetic friction: $f_{k} = \mu_{k} N$. Assuming $\mu_{k} = \mu_{s} = 0.4$,we get $f_{k} = 0.4 	imes mg 	imes 0.5 = 0.2 mg = \frac{mg}{5}$.

$A$ solid cylinder of mass $m$ is wrapped with an inextensible light string and is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is: [The coefficient of static friction,$\mu_{s}$,is $0.4$]

Similar Questions

$A$ plane is inclined at an angle of $30^{\circ}$ with the horizontal. If a sphere rolls down this plane without slipping,what will be the linear acceleration of the sphere?

$A$ ball of radius $11 \ cm$ and mass $8 \ kg$ rolls from rest down a ramp of length $2 \ m$. The ramp is inclined at $35^{\circ}$ to the horizontal. When the ball reaches the bottom,its velocity is .......... $m/s$. $(\sin 35^{\circ} = 0.57)$

$A$ disc of radius $20 \, cm$ and mass $0.5 \, kg$ is rolling on an inclined plane with an angle of inclination $45^{\circ}$. Find the friction force required for the disc to perform pure rolling.

$A$ disc rolls without slipping on an inclined plane. What fraction of its total energy is in the form of rotational kinetic energy?

Vedclass Test Series

Exam Paper Generator

Online Exam Module