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 ...... $m/s$

A small object placed on a rotating horizontal turn table just slips when it is placed at a distance $4\, cm$ from the axis of rotation. If the angular velocity of the turn-table is doubled, the object slips when its distance from the axis of rotation is

A mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity ${\omega _0}$. If the length of the string and angular velocity are doubled, the tension in the string which was initially ${T_0}$ is now

A motorcyclist of mass m is to negotiate a curve of radius r with a speed v. The minimum value of the coefficient of friction so that this negotiation may take place safely, is

A $100 \,kg$ car is moving with a maximum velocity of $9 \,m/s$ across a circular track of radius $30\,m$. The maximum force of friction between the road and the car is ........ $N$

A block of mass $10\; \mathrm{kg}$ is in contact against the inner wall of a hollow cylindow cylindrical drum of radius $1 \;\mathrm{m}$. The coeffident of friction between the block and the inner wall of the cylinder is $0.1$. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be: ......$rad/s$ $\left(g-10 m / s^{2}\right)$