A cylinder of mass m radius R is spined to a clockwise angular velocity `omega_(o)` and then gently placed on an inclined plane for which coefficient of friction `mu = tan theta, theta` is the angle of inclined plane with the horizontal. The centre of mass of cylinder will remain stationary for time

An cylinder of mass m is rotated about its axis by an angular velocity omega and lowered gently on an inclined plane as shown in figure. Then : .

A mass placed on an inclined place is just in equilibrium. If mu is coefficient of friction of the surface, then maximum inclination of the plane with the horizontal is

A mass placed on an inclined place is just in equilibrium. If mu is coefficient of friction of the surface, then maximum inclination of the plane with the horizontal is

A ball of mass m and radius R rotating with an angular speed omega_(0) as shown in the figure is placed on an incline plane. Coefficient of friction is 1// sqrt(3) and the length of the incline plane is L. The angle of inclination of the plane is theta = 30^(@) . Find after what time it will reach at the bottom most point.

A uniform solid sphere of mass m and radius 'R' is imparted an initial velocity v_(0) and angular omega_(0) = (2v_(0))/(R ) and then placed on a rough inclined plane of inclination 'theta' and coefficient of friction mu = 2 tan theta as shown. The time after which the sphere will start rolling without slipping is

A uniform solid sphere of mass m and radius 'R' is imparted an initial velocity v_(0) and angular omega_(0) = (2v_(0))/(R ) and then placed on a rough inclined plane of inclination 'theta' and coefficient of friction mu = 2 tan theta as shown. The time after which the sphere will start rolling without slipping is

Show that a cylinder will slip on an inclined plane if the coefficient of static friction between the plane and the cylinder is less than 1/3tantheta where theta is the angle of the inclination with the horizontal.