Circular Motion PYQs Set 1 (PDF)

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Mere Teacher · Previous Year Questions JEE Main Physics · Circular Motion · Set 1 (Q1-30)
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1. $A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8 \times 1 0^{-4} J by the end of the second revolution after the beginning of the motion ?$ (1) $0.2 m/ s^{2}$ (2) $0.1 m/ s^{2}$ (3) $0.15 m/ s^{2}$ (4) $0.18 m/ s^{2}$ 2. $The minimum horizontal speed with which a body must be projected, so that it goes around a smooth vertical circular track of radius 4 m is (g = 9.8 ms^{- 2})$ (1) $7 ms^{- 1}$ (2) $14 ms^{- 1}$ (3) $0.7 ms^{- 1}$ (4) $1.4 ms^{- 1}$ 3. $A particle moving with uniform speed in a circular path maintains [NEET 2024]$ (1) $Constant velocity$ (2) $Constant acceleration$ (3) $Constant velocity but varying acceleration$ (4) $Varying velocity and varying acceleration$ 4. $A particle is moving at a speed of 10 m / s in a circular motion. The radius of the path is 2 m and mass of the particle is 2 kg . The centripetal force of the particle is$ (1) $50 N$ (2) $150 N$ (3) $100 N$ (4) $170 N$ 5. $A car of mass m is moving on a level circular track of radius R. If µ_{s} represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by :$ (1) $μ_{s} m R g$ (2) $R g / μ_{s}$ (3) $m R g / μ_{s}$ (4) $μ_{s} R g$ 6. $A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45º, the speed of the car is :$ (1) $20 m s^{-1}$ (2) $30 m s^{-1}$ (3) $5 m s^{-1}$ (4) $10 m s^{-1}$ 7. $A car is travelling at 30 ms^{- 1} speed on a circular road of radius 300 m . If its speed is increasing at the rate of 4 ms^{- 2}, then its acceleration is$ (1) $2.7 ms^{- 2}$ (2) $3 ms^{- 2}$ (3) $4 ms^{- 2}$ (4) $5 ms^{- 2}$ 8. $A man is slipping on a frictionless inclined plane and a bag falls down from the same height. Then the velocity of both is related as$ (1) $v_{B} > v_{m}$ (2) $v_{B} < v_{m}$ (3) $v_{B} = v_{m}$ (4) $v_{B} and v_{m} can’t be related$ 9. $An object dropped in a stationary lift takes time t_{1} to reach the floor. It takes time t_{2} when lift is moving up with constant acceleration. Then$ (1) $t_{2} > t_{1}$ (2) $t_{1} > t_{2}$ (3) $t_{1} \approx t_{2}$ (4) $t_{1} = t_{2}$ 10. $The difference between angular speed of minute hand and second hand of a clock is$ (1) $\frac{59 π}{900} rad / s$ (2) $\frac{59 π}{1800} rad / s$ (3) $\frac{59 π}{2400} rad / s$ (4) $\frac{59 π}{3600} rad / s$ 11. $An electric fan has blades of length 30 cm measured from the axis of rotation. If the fan is rotating at 120 rpm, the acceleration of a point on the tip of the blade is$ (1) $1600 m s^{- 2}$ (2) $47.4 m s^{- 2}$ (3) $23.7 m s^{- 2}$ (4) $50.55 m s^{- 2}$ 12. $In non-uniform circular motion, the ratio of tangential to radial acceleration is r = radius of circle, v = speed of the particle, α = angular acceleration)$ (1) $\frac{α ^{2} r ^{2}}{v}$ (2) $\frac{α ^{2} r}{v ^{2}}$ (3) $\frac{α r ^{2}}{v ^{2}}$ (4) $\frac{v ^{2}}{r ^{2} α}$ 13. $A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 seconds, what is the magnitude and direction of acceleration of the stone?$ (1) $π^{2} m s^{- 2} and direction along the radius towards the center$ (2) $π^{2} m s^{- 2} and direction along the radius away from the center$ (3) $π^{2} m s^{- 2} and direction along the tangent to the circle$ (4) $π^{2} /4 m s^{- 2} and direction along the radius towards the center.$ 14. $A particle moves such that its position vector r \to (t) = cos ωt i^+ sin ωt j^where ω is a constant and t is time. Then which of the following statements is true for the velocity v \to (t) and acceleration a \to (t) of the particle:$ (1) $v \to is perpendicular to r \to and a \to is towards origin$ (2) $v \to and a \to are perpendicular to r \to$ (3) $v \to is parallel to r \to and a \to parallel to r \to$ (4) $v \to is perpendicular to r \to and a \to is away from origin.$ 15. $Simultaneously, from the top of a tower, when ball-1 is thrown horizontally and ball-2 is just dropped, in the absence of air resistance which among the following options is correct?$ (1) $Ball-1 reaches the ground first.$ (2) $Ball-2 reaches the ground first.$ (3) $Both will reach the ground simultaneously.$ (4) $Either ball-1 or ball-2 reach the ground first depending on which ever is heavier$ 16. $A mosquito is moving with a velocity v = 0.5 t^{2} i + 3 t j + 9 k m / s and accelerating in uniform conditions.What will be the direction of mosquito after 2 s ?$ (1) $tan^{- 1} (\frac{2}{3}) from x - axis$ (2) $tan^{- 1} (\frac{85}{6}) from y - axis$ (3) $tan^{- 1} (\frac{5}{2}) from y - axis$ (4) $tan^{- 1} (\frac{5}{2}) from x - axis$ 17. $If the radii of circular paths of two particles of same mass are in the ratio of 1 : 2, then to have a constant centripetal force, the ratio of their speeds should be$ (1) $4 : 1$ (2) $1 : 2$ (3) $1 : 4$ (4) $2 : 1$ 18. $A particle at rest starts moving with constant angular acceleration 4 rad / s^{2} in circular path. At what time the magnitude of its tangential acceleration and centrifugal acceleration will be equal?$ (1) $0.4 s$ (2) $0.5 s$ (3) $0.8 s$ (4) $1.0 s$ 19. $A car is travelling with linear velocity ' V' on a circular road of radius 'r'. If its velocity is increasing at a rate of ' a' ms^{- 2}, then the resultant acceleration will be$ (1) $(\frac{v ^{2}}{r ^{2}} - a^{2})$ (2) $(\frac{v ^{4}}{r ^{2}} + a^{2})$ (3) $(\frac{V ^{4}}{r ^{2}} - a^{2}) .$ (4) $(\frac{v ^{2}}{r ^{2}} + a^{2})$ 20. $A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle θ to the horizontal, the maximum height attained by it equals 4 R . The angle of projection θ is then given by [NEET 2021]$ (1) $θ = cos^{- 1} [\frac{g T ^{2}}{π ^{2} R}]^{1/2}$ (2) $θ = cos^{- 1} [\frac{π ^{2} R}{g T ^{2}}]^{1/2}$ (3) $θ = sin^{- 1} [\frac{π ^{2} R}{g T ^{2}}]^{1/2}$ (4) $θ = sin^{- 1} [\frac{2 g T ^{2}}{π ^{2} R}]^{1/2}$ 21. $A gramophone record is revolving with an angular velocity ω. A coin is placed at a distance r from the center of the record. The static coefficient of friction is µ. The coin will revolve with the record if$ (1) $r = µ g ω^{2}$ (2) $r = \frac{ω ^{2}}{μg}$ (3) $r \leq \frac{μg}{ω ^{2}}$ (4) $r \geq \frac{μg}{ω ^{2}}$ 22. $A particle initially at origin starts moving in xy-plane has velocity component V = (6 + 2 t) i + (4 + 23 t) j m / s . Acceleration of the particle in m / s^{2} is [x, y are measured in metres, t in seconds, respectively]$ (1) $(6 + 2 t) i + (4 + 23 t) j$ (2) $(6 + 2 t) i + 23 j$ (3) $2 i + 23 j$ (4) $2 i + 23 k$ 23. $If the radius of curvature of the path of two particles of same mass are in the ratio 3:4, then in order to have constant centripetal force, their velocities will be in the ratio of:$ (1) $3 : 2$ (2) $1 : 3$ (3) $3 : 1$ (4) $2 : 3$ 24. $A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the hand (in units of ms^{- 2}) is of the order of$ (1) $10^{- 1}$ (2) $10^{- 2}$ (3) $10^{- 4}$ (4) $10^{- 3}$ 25. $The ratio of angular speed of a second-hand to the hour-hand of a watch is$ (1) $60 : 1$ (2) $72 : 1$ (3) $720 : 1$ (4) $3600 : 1$ 26. $Two particles A and B are moving in uniform circular motion in concentric circles of radii r_{A} and r_{B} with speed v_{A} and v_{B} respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be [NEET 2019]$ (1) $1 : 1$ (2) $r_{A} : r_{B}$ (3) $v_{A} : v_{B}$ (4) $r_{B} : r_{A}$ 27. $The x and y coordinates of the particle at any time are x = 5 t - 2 t^{2} and y = 10 t respectively, where x and y are in metres and t in seconds. The acceleration of the particle at t = 2 s is [NEET 2017]$ (1) $0$ (2) $5 m / s^{2}$ (3) $- 4 m / s^{2}$ (4) $- 8 m / s^{2}$ 28. $In uniform circular motion, which of the following statement is wrong?$ (1) $Work' done during one complete cycle is zero.$ (2) $Centripetal force acting towards the centre of circle.$ (3) $Angular velocity is constant.$ (4) $Tangential velocity is constant.$ 29. $A merry-go-round rotating at a constant angular speed completes 9 rotations in 18 seconds. What is its angular speed?$ (1) $π /2 rad / s$ (2) $π rad / s$ (3) $2 π rad / s$ (4) $3 π rad / s$ 30. $A particle is performing U.C.M along the circumference of a circle of diameter 50 cm with frequency 2 Hz . The acceleration of the particle in m / s^{2} is$ (1) $2 π^{2}$ (2) $8 π^{2}$ (3) $π^{2}$ (4) $4 π^{2}$