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A hemispherical bowl of radius $r$ is set rotating about its axis of symmetry in vertical. A small block kept in the bowl rotates with bowl without slipping on its surface. If the surface of the bowl is smooth and the angle made by the radius through the block with the vertical is $\theta$, then find the angular speed at which the ball is rotating.
A block of mass $M$ rests on a rough horizontal table. A steadily increasing horizontal force is applied such that the block starts to slide on the table without toppling. The force is continued even after sliding has started. Assume the coefficients of static and kinetic friction between the table and the block to be equal. The correct representation of the variation of the frictional force $f$, exerted by the table on the block with time $t$ is given by
A disc with a flat small bottom beaker placed on it at a distance $R$ from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $\mu$. The beaker will revolve with the disc if
A car of mass $800 \,kg$ moves on a circular track of radius $40\, m$. If the coefficient of friction is $0.5$, then maximum velocity with which the car can move is ......... $m/s$
A small ball of mass $m$ starts at a point $A$ with speed $v_0$ and moves along a frictionless track $AB$ as shown. The track $BC$ has coefficient of friction $\mu $. The ball comes to stop at $C$ after travelling a distance $L$ which is
A plank is resting on a horizontal ground in the northern hemisphere of the earth at a $45^{\circ}$ latitude. Let the angular speed of the earth be $\omega$ and its radius $r_e$. The magnitude of the frictional force on the plank will be
A small body slips, subject to the force of friction, from point $A$ to point $B$ along two curved surfaces of equal radius, first along route $1,$ then along route $2$. Friction does not depend on the speed and the coefficient of friction on both routes is the same. In which case will the body’s speed at $B$ be greater?
A body is pulled along a rough horizontal surface with a velocity $6\,m/s$. If the body comes to rest after travelling $9\,m$ , then coefficient of sliding friction, is- (Take $g = 10\,m/s^2$ )
The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by