Uniform Circular Motion PYQs: JEE Mains Physics

Showing 1–20 of 20 questions

1. 1.
   A string of length \(L\) is fixed at one end and carries a mass of \(M\) at the other end. The mass makes \(\left(\frac{3}{\pi}\right)\) rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is \(\ldots\ldots\) ML. 2025 Hard
2. 2. A tube of length 1 m is filled completely with an ideal liquid of mass 2 M , and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is \(\sqrt{\frac{\mathrm{F}}{\alpha \mathrm{M}}}\) in SI unit. The value of \(\alpha\) is __________. 2025 Hard
3. 3. A ball of mass \(0.5 \mathrm{~kg}\) is attached to a string of length \(50 \mathrm{~cm}\). The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is \(400 \mathrm{~N}\). The maximum possible value of angular velocity of the ball in rad/s is _______. 2024 Hard
4. 4. A clock has \(75 \mathrm{~cm}, 60 \mathrm{~cm}\) long second hand and minute hand respectively. In \(30\) minutes duration the tip of second hand will travel \(x\) distance more than the tip of minute hand. The value of \(x\) in meter is nearly _______. (Take \(\pi=3.14\) ) 2024 Hard
5. 5. A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius \(9 \mathrm{~m}\) and completes \(120\) revolutions in \(3\) minutes. The magnitude of centripetal acceleration of monkey is _______ (in \(\mathrm{m} / \mathrm{s}^2\) ). 2024 Hard
6. 6. A particle moving in a circle of radius \(R\) with uniform speed takes time \(\mathrm{T}\) to complete one revolution. If this particle is projected with the same speed at an angle \(\theta\) to the horizontal, the maximum height attained by it is equal to \(4 R\). The angle of projection \(\theta\) is then given by _______. 2024 Hard
7. 7. A stone of mass \(900 \mathrm{~g}\) is tied to a string and moved in a vertical circle of radius \(1 \mathrm{~m}\) making \(10\  \mathrm{rpm}\). The tension in the string, when the stone is at the lowest point is _______. (if \(\pi^2=9.8\) and \(g=9.8 \mathrm{~m} / \mathrm{s}^2\) ) 2024 Hard
8. 8. A particle is moving with constant speed in a circular path. When the particle turns by an angle \(90^{\circ}\), the ratio of instantaneous velocity to its average velocity is \(\pi: x \sqrt{2}\). The value of \(x\) will be \(.........\) 2023 Hard
9. 9. A stone tied to \(180 cm\) long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is \(\frac{1936}{ x }\,ms ^{-2}\). The value of \(x.........\left(\text { Take } \pi=\frac{22}{7}\right)\) 2023 Easy
10. 10. An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at \(x =+2\,m\), its velocity is \(-4 \hat{ j }\, m / s\). The object's velocity \((v)\) and acceleration \((a)\) at \(x =-2\,m\) will be 2023 Medium
11. 11. As shown in the figure, a particle is moving with constant speed \(\pi\,m / s\). Considering its motion from \(A\) to \(B\), the magnitude of the average velocity is:
    2023 Hard
12. 12. For particle \(P\) revolving round the centre \(O\) with radius of circular path \(r\) and angular velocity \(\omega\), as shown in below figure, the projection of \(OP\) on the \(x\)-axis at time \(t\) is \(.................\).
    2023 Easy
13. 13. A boy ties a stone of mass \(100 \,g\) to the end of a \(2\) \(m\) long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of \(80 \,N\). If the maximum speed with which the stone can revolve is \(\frac{ K }{\pi} rev\). / \(min\). The value of \(K\) is (Assume the string is massless and unstretchable) 2022 Medium
14. 14. A fly wheel is accelerated uniformly from rest and rotates through \(5 \,rad\) in the first second. The angle rotated by the fly wheel in the next second, will be.........\(rad\) 2022 Easy
15. 15. A huge circular arc of length \(4.4\) \(ly\) subtends an angle \('4 {s}'\) at the centre of the circle. How long it would take for a body to complete \(4\) revolution if its speed is \(8 \;AU\;per\, second \;?\) Given : \(1\, {ly}=9.46 \times 10^{15} \,{m},\) \(\, {AU}=1.5 \times 10^{11}\, {m}\) 2021 Hard
16. 16. A particle is moving with uniform speed along the circumference of a circle of radius \(R\) under the action of a central fictitious force \(F\) which is inversely proportional to \(R ^{3}\). Its time period of revolution will be given by 2021 Hard
17. 17. A particle of mass \({m}\) is suspended from a ceiling through a string of length \(L\). The particle moves in a horizontal circle of radius \(r\) such that \({r}=\frac{{L}}{\sqrt{2}}\). The speed of particle will be: 2021 Hard
18. 18. A smooth wire of length \(2\pi r\) is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed \(\omega\) about the vertical diameter \(AB\), as shown in figure, the bead is at rest with respect to the circular ring at position \(P\) as shown. Then the value of \(\omega^2\) is equal to
    2019 Hard
19. 19. A conical pendulum of length \(1\,m\) makes an angle \(\theta \, = 45^o\) w.r.t. \(Z-\) axis and moves in a circle in the \(XY\) plane.The radius of the circle is \(0.4\, m\) and its centre is vertically below \(O\). The speed of the pendulum, in its circular path, will be ..... \(m/s\) (Take \(g\, = 10\, ms^{-2}\))
    2017 Hard
20. 20. A particle is released on a vertical smooth semicircular track from point \(X\) so that \(OX\) makes angle \(\theta \) from the vertical ( see figure). The normal reaction of the track on the particle vanishes at point \(Y\) where \(OY\) makes angle \(\phi \) with the horizontal. Then
    2014 Hard

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