Circular Motion - Mechanics - Physics PYQ

A motor cyclist wants to drive in horizontal circles on the vertical inner surface of a large cylindrical wooden well of radius \(8.0 \mathrm{~m}\), with minimum speed of \(5 \sqrt{5} \mathrm{~ms}^{-1}\). The minimum value of coefficient of friction between the tyres and the wall of the well must be \(\left(g=10 \mathrm{~ms}^{-2}\right)\)

A 500 kg car takes a round turn of radius 50 m with a velocity of 36 km/h. The centripetal force acting on the car is

Assertion (A) Two identical trains move in opposite senses in equatorial plane with same speeds relative to the Earth’s surface. They have equal magnitude of normal reaction.

Reason (R) The trains have different centripetal accelerations due to different speeds.

A body of mass 10 kg is attached to a wire of 0.3 m length. The breaking stress is 4.8 \(\times\) 10\(^7\) Nm\(^{-2}\). The area of cross-section from the wire is 10\(^{-6}\) m\(^{2}\). The maximum angular velocity with which it can be rotated in a horizontal circle is

If a particle of mass ' $m$ ' covers half of the horizontal circle with constant speed ' $v$ ', then the change in its kinetic energy is

Ratio of angular velocity of hour hand of a watch and the angular velocity of rotation of Earth is

A wire of length 2.5 m is fixed at one end and a box of mass 4 kg is tied at the other end. If the wire rotates in a horizontal circle about the fixed end with $\frac{2}{\pi}$ rotations per second, then the tension in the wire is

If a stone of mass 0.5 kg tied to one end of a wire is whirled in a circular path of radius 2 m with a speed $40 \mathrm{rev} / \mathrm{min}$ in a horizontal plane, then the tension in the wire is nearly

A block of mass $m$ and charge $q$ is connected to a point owith an inextensible string. This system is on a horizontal table. An electric field $E$ is applied perpendicular to the string and in the plane of the horizontal table. The tension in the string when it becomes parallel to the electric field is