A $500\, kg$ crane takes a turn of radius $50 \,m$ with velocity of $36 \,km/hr.$ The centripetal force is ......... $N$

A small mass $'m'$ rests at the edge of a horizontal disc of radius $'R'$ . The coefficient of static friction between mass and the disc is $\mu $ . The disc is rotated about its axis at an angular velocity such that the mass slides off the disc and lands on the floor $'h'$ meters below. What was its horizontal distance of travel from the point it left the disc?

A cyclist moves in a circular track of radius $100$ m. If the coefficient of friction is $0.2$, then the maximum velocity with which the cyclist can take the turn with leaning inwards is ...... $m/s$ 

A vehicle is moving on a track with constant speed as shown in figure. The apparent weight of the vehicle is 

A car is moving with a constant speed of $20\,m / s$ in a circular horizontal track of radius $40\,m$. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take $g =10$ $\left.m / s ^2\right)$

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.