Circular Motion

A car moving with a speed of 54 km / h takes a turn of radius 20 m . A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take \(g=10m/{s}^{2}\) )

[JEE Main 2026, 8 Apr (Shift 2)]

A train is moving with a speed of \(12 m / s\) on rails which are \(1.5 m\) apart. To negotiate a curve of radius \(400 m\), the height by which the outer rail should be raised with respect to the inner rail is: (Given, \(g =10 m / s ^2\)):

A stone of mass \(900g\) is tied to a string and moved in a vertical circle of radius\(1m\) making\(10rpm\). The tension in the string, when the stone is at the lowest point is (if \({\pi }^{2}=9.8\) and \(g=9.8m/{s}^{2}\)):

An object is performing vertical circular motion. If its velocity at the topmost point is given by:

\({v}_{\text{top}}=n\sqrt{gl},\ n>1\)

Determine the ratio of the kinetic energy at the bottom to that at the top.​

A stone of mass \(1\mathrm{kg}\) is tied to end of a massless string of length \(1\mathrm{m}\). If the breaking tension of the string is \(400\mathrm{N}\), then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is:

[JEE Main 2023, 31 Jan (Shift 2)]

A stone of mass \(1\mathrm{kg}\) is tied to end of a massless string of length \(1\mathrm{m}\). If the breaking tension of the string is \(400\mathrm{N}\), then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is:

A car is moving on a horizontal curved road with radius \(50 m\). The approximate maximum speed of car will be, if friction coefficient between tyres and road is 0.34 . [Take \(g=10 ms ^{-2}\) ]

[JEE Main 2023, 29 Jan (Shift 1)]

A particle moves such that its position vector \(\vec{r}(t)=\cos \omega t \hat{i}+\sin \omega t \hat{j}\) where \(\omega\) is a constant and \(t\) is time. Then which of the following statements is true for the velocity \(\vec{v}(t)\) and acceleration \(\vec{a}(t)\) of the particle:

A child of mass \(5 kg\) is going round a merry-go-round that makes 1 rotation in \(3.14 s\). The radius of the merry-go-round is \(2 m\). The centrifugal force on the child will be:

[JEE Main 2023, 6 Apr (Shift 2)]

Statement I: A cyclist is moving on an unbanked road with a speed of \(7 kmh ^{-1}\) and takes a sharp circular turn along a path of radius of \(2 m\) without reducing the speed. The static friction coefficient is 0.2 . The cyclist will not slip and pass the curve. \(\left(g=9.8 m / s ^2\right)\)
Statement II: If the road is banked at an angle of \(45^{\circ}\), cyclist can cross the curve of \(2 m\) radius with the speed of \(18.5 kmh ^{-1}\) without slipping.
In the light of the above statements, choose the correct answer from the options given below.

[JEE Main 2021, 16 Mar (Shift 2)]