Vertical Circular Motion PYQs: JEE Mains Physics

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1. 1. In case of vertical circular motion of a particle by a thread of length \(r\) if the tension in the thread is zero at an angle \(30^{\circ}\) shown in figure, the velocity at the bottom point (A) of the circular path is ( \(g =\) gravitational acceleration)
   2026 Medium
2. 2. A bob of mass \(m\) is suspended at a point \(O\) by a light string of length \(l\) and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity \(v_0\) at the point ' A ', the string becomes slack when, the bob reaches at the point ' D '. The ratio of the kinetic energy of the bob at the points \(B\) and \(C\) is ______ -.
   
   
   2025 Medium
3. 3. A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point \(A\) is \(10 \mathrm{~m} / \mathrm{s}\). The ratio of its kinetic energies at point \(B\) and \(C\) is :
   
   (Take acceleration due to gravity as \(10 \mathrm{~m} / \mathrm{s}^2\) ) 2025 Medium
4. 4. A body of mass ' \(m\) ' connected to a massless and unstretchable string goes in verticle circle of radius ' \(R\) 'under gravity \(g\). The other end of the string is fixed at the center of circle. If velocity at top of circular path is \(n \sqrt{g R}\), where, \(n \geqslant 1\), then ratio of kinetic energy of the body at bottom to that at top of the circle is 2025 Hard
5. 5. A bob of mass ' \(m\) ' is suspended by a light string of length ' \(L\) '. It is imparted a minimum horizontal velocity at the lowest point \(A\) such that it just completes half circle reaching the top most position B. The ratio of kinetic energies \(\frac{(\text { K.E. })_A}{(\text { K.E. })_B}\) is _______.
   2024 Hard
6. 6. A closed circular tube of average radius \(15\,cm\), whose inner walls are rough, is kept in vertical plane. A block of mass \(1\,kg\) just fit inside the tube. The speed of block is \(22\,m / s\), when it is introduced at the top of tube. After completing five oscillations, the block stops at the bottom region of tube. The work done by the tube on the block is \(......J\). [Given \(g=10\,m / s ^2\) ]
   2023 Hard
7. 7. A pendulum of length \(2 \; m\) consists of a wooden bob of mass \(50 \; g\). A bullet of mass \(75 \; g\) is fired towards the stationary bob with a speed \(v\). The bullet emerges out of the bob with a speed \(\frac{v}{3}\) and the bob just completes the vertical circle. The value of \(v\) is \(\dots \; ms ^{-1}\). (if \(g =10 \; m / s ^{2}\) ) 2022 Hard
8. 8. A stone tide to a string of length \(L\) is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed \(u\). The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is \(\sqrt{ x \left( u ^{2}- gL \right)}\). The value of \(x\) is ............. 2022 Medium
9. 9. A small block slides down from the top of hemisphere of radius \(R=3\, {m}\) as shown in the figure. The height \('h'\) at which the block will lose contact with the surface of the sphere is \(.............  \;\;m\). (Assume there is no friction between the block and the hemisphere)
   2021 Hard
10. 10. A small bob tied at one end of a thin string of length \(1\, m\) is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio \(5: 1 .\) The velocity of the bob at the height position is ............. \(m / s\) (Take \(\left.g=10 \,m / s ^{2}\right)\) 2021 Hard

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