Rolling On Inclined Plane PYQs: JEE Mains Physics

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1. 1. A LCR series circuit driven with \(E_{rms} = 90\) V at frequency \(f_d = 30\) Hz has resistance \(R = 80\,\Omega\), an inductance with inductive reactance \(X_L = 20.0\,\Omega\) and capacitance with capacitive reactance \(X_C = 80.0\,\Omega\). The power factor of the circuit is _______. 2026 Medium
2. 2. A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is \(\sqrt{\frac{x}{5}}\) where \(\mathrm{x}=\) _____ 2025 Medium
3. 3. A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be \(t_1\) and \(t_2\), respectively, then... 2025 Easy
4. 4. A solid sphere of mass ' \(m\) ' and radius ' \(r\) ' is allowed to roll without slipping from the highest point of an inclined plane of length ' \(L\) ' and makes an angle \(30^{\circ}\) with the horizontal. The speed of the particle at the bottom of the plane is \(v_1\). If the angle of inclination is increased to \(45^{\circ}\) while keeping \(L\) constant. Then the new speed of the sphere at the bottom of the plane is \(v_2\). The ratio \(v_1^2: v_2^2\) is: 2025 Hard
5. 5. A uniform solid cylinder of mass ' \(m\) ' and radius ' \(r\) ' rolls along an inclined rough plane of inclination \(45^{\circ}\). If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be 2025 Medium
6. 6. A circular disc reaches from top to bottom of an inclined plane of length \(l\). When it slips down the plane, if takes \(\mathrm{t} \mathrm{s}\). When it rolls down the plane then it takes \(\left(\frac{\alpha}{2}\right)^{1 / 2} \mathrm{t} s\), where \(\alpha\) is. _______. 2024 Hard
7. 7. A cylinder is rolling down on an inclined plane of inclination \(60^{\circ}\). It's acceleration during rolling down will be \(\frac{\mathrm{x}}{\sqrt{3}} \mathrm{~m} / \mathrm{s}^2\), where \(\mathrm{x}=\)___________. (use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) ). 2024 Hard
8. 8. A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is \(\frac{7}{\mathrm{x}}\) where \(\mathrm{x}\) is___________. 2024 Hard
9. 9. A solid cylinder is released from rest from the top of an inclined plane of inclination \(30^{\circ}\) and length \(60\,cm\). If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is \(...........ms ^{-1}\). (Given \(g =10\,ms ^{-2}\))
   2023 Medium
10. 10. A solid cylinder and a solid sphere, having same mass \(M\) and radius \(R\), roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be. 2022 Medium
11. 11. A circular disc reaches from top to bottom of an inclined plane of length \('L'.\) When it slips down the plane, it takes time \('t_{1}'\). when it rolls down the plane, it takes time \(t_{2}\). The value of \(\frac{t_{2}}{t_{1}}\) is \(\sqrt{\frac{3}{x}}\). The value of \(x\) will be .... . 2021 Hard
12. 12. A solid disc of radius \('a'\) and mass \('m'\) rolls down without slipping on an inclined plane making an angle \(\theta\) with the horizontal. The acceleration of the disc will be \(\frac{2}{ b } g \sin \theta\) where \(b\) is \(........\). (Round off to the Nearest Integer) \(( g =\) acceleration due to gravity) \((\theta=\) angle as shown in figure \()\)
    2021 Hard
13. 13. A sphere of mass \(2\,kg\) and radius \(0.5\, m\) is rolling with an initial speed of \(1 \,ms ^{-1}\) goes up an inclined plane which makes an angle of \(30^{\circ}\) with the horizontal plane, without slipping. How low will the sphere take to return to the starting point \(A\) ? (in \(second\))
    2021 Hard
14. 14. Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter. The correct statement for this situation is:- 2021 Medium
15. 15. The following bodies, \((1)\) a ring \((2)\) a disc \((3)\) a solid cylinder \((4)\) a solid sphere, of same mass \(m\) and radius \(R\) are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is ........... [Mark the body as per their respective numbering given in the question]
    2021 Hard
16. 16. The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal place: \((i)\) a ring of radius \(R,\,(ii)\) a solid cylinder of radius \(\frac {R}{2}\)  nd \((iii)\) a solid sphere of radius \(\frac {R}{4}.\) If, in each case, the speed of the center of mass at bottom of the incline is same, the ratio of the maximum heights they climb is 2019 Hard
17. 17. The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal place: \((i)\) a ring of radius \(R,\,(ii)\) a solid cylinder of radius \(\frac {R}{2}\)  nd \((iii)\) a solid sphere of radius \(\frac {R}{4}.\) If, in each case, the speed of the center of mass at bottom of the incline is same, the ratio of the maximum heights they climb is 2019 Hard
18. 18. A cylinder of mass \(M_c\) and sphere of mass \(M_s\) are placed at points \(A\) and \(B\) of two inclines, respectively (See Figure). If they roll on the incline without sipping such that their accelerations are the same, then the ratio \(\frac{{\sin \,{\theta _c}}}{{\sin \,{\theta _s}}}\) is
    2014 Hard
19. 19. A cylinder of mass \(M_c\) and sphere of mass \(M_s\) are placed at points \(A\) and \(B\) of two inclines, respectively (See Figure). If they roll on the incline without sipping such that their accelerations are the same, then the ratio \(\frac{{\sin \,{\theta _c}}}{{\sin \,{\theta _s}}}\) is
    2014 Hard
20. 20. A tennis ball (treated as hollow spherical shell) starting from \(O\) rolls down a hill. At point \(A\) the ball becomes air borne leaving at an angle of \(30^o\) with the horizontal. The ball strikes the ground at \(B\). What is the value of the distance \(AB\) ? (Moment of inertia of a spherical shell of mass \(m\) and radius \(R\) about its diameter .......... \(m\). \(= \frac {2}{3}\,mR^2\))
    2013 Hard
21. 21. A tennis ball (treated as hollow spherical shell) starting from \(O\) rolls down a hill. At point \(A\) the ball becomes air borne leaving at an angle of \(30^o\) with the horizontal. The ball strikes the ground at \(B\). What is the value of the distance \(AB\) ? (Moment of inertia of a spherical shell of mass \(m\) and radius \(R\) about its diameter .......... \(m\). \(= \frac {2}{3}\,mR^2\))
    2013 Hard

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