Circular motion with and without Friction PYQs: JEE Mains Physics

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1. 1. A large drum having radius \(R\) is spinning around its axis with angular velocity \(\omega\), as shown in figure. The minimum value of \(\omega\) so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass M is \(\mu\), is :
   2026 Hard
2. 2. A car of mass ' \(m\) ' moves on a banked road having radius ' \(r\) ' and banking angle \(\theta\). To avoid slipping from banked road, the maximum permissible speed of the car is \(v_0\). The coefficient of friction \(\mu\) between the wheels of the car and the banked road is 2025 Medium
3. 3. A car of \(800 \mathrm{~kg}\) is taking turn on a banked road of radius \(300 \mathrm{~m}\) and angle of banking \(30^{\circ}\). If coefficient of static friction is \(0.2\) then the maximum speed with which car can negotiate the turn safely which? \(\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sqrt{3}=1.73\right)\) 2024 Hard
4. 4. A coin is placed on a disc. The coefficient of friction between the coin and the disc is \(\mu\). If the distance of the coin from the center of the disc is \(r\), the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is _______. 2024 Hard
5. 5. A train is moving with a speed of \(12 \mathrm{~m} / \mathrm{s}\) on rails which are \(1.5 \mathrm{~m}\) apart. To negotiate a curve radius \(400 \mathrm{~m}\), the height by which the outer rail should be raised with respect to the inner rail is (Given, \(g=\) \(10 \mathrm{~m} / \mathrm{s}^2\) ) : 2024 Hard
6. 6. If the radius of curvature of the path of two particles of same mass are in the ratio \(3:4,\) then in order to have constant centripetal force, their velocities will be in the ratio of: 2024 Hard
7. 7. A car is moving on a horizontal curved road with radius \(50\,m\). The approximate maximum speed of car will be \(............\,ms^{-1}\), if friction between tyres and road is \(0.34.\left[\right.\) Take \(\left.g =10 ms ^{-2}\right]\) 2023 Medium
8. 8. 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 \(g =10\) \(\left.m / s ^2\right)\) 2023 Medium
9. 9. A vehicle of mass \(200\,kg\) is moving along a levelled curved road of radius \(70\,m\) with angular velocity of \(0.2\,rad / s\). The centripetal force acting on the vehicle is \(.........\,N\) 2023 Medium
10. 10. A curved in a level road has a radius \(75\, m\). The maximum speed of a car turning this curved road can be \(30 \,m / s\) without skidding. If radius of curved road is changed to \(48\, m\) and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be .........\(m / s\). 2022 Medium
11. 11. 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  2022 Medium

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