Circular Motion PYQs Set 2 (PDF)

Set 2 of 3 · Questions 31-60 of 90

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Mere Teacher · Previous Year Questions JEE Main Physics · Circular Motion · Set 2 (Q31-60)
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31. $A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius 9 m and completes 120 resolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is ( in m / s^{2}):$ (1) $57600 π^{2} ms^{- 2}$ (2) $Zero$ (3) $4 π^{2} ms^{- 2}$ (4) $16 π^{2} ms^{- 2}$ 32. $In U.C.M., when time interval δt \to 0, the angle between change in velocity (δ v) and linear velocity (v) will be$ (1) $0^{\circ}$ (2) $90^{\circ}$ (3) $180^{\circ}$ (4) $45^{\circ}$ 33. $Two cars of masses m_{1} and m_{2} are moving in circles of radii r_{1} and r_{2}, respectively. Their speeds are such that they make complete circles in the same time t . The ratio of their centripetal acceleration is:$ (1) $m_{1} r_{1} = m_{2} r_{2}$ (2) $m_{1} : m_{2}$ (3) $r_{1} : r_{2}$ (4) $1 : 1$ 34. $The angular acceleration of a body, moving along the circumference of a circle, is [NEET 2023]$ (1) $along the radius towards the center$ (2) $along the tangent to its position$ (3) $along the axis of rotation$ (4) $along the radius, away from center$ 35. $Two particles A and B are moving in uniform circular motion in concentric circles of radii r_{A} and r_{B} with speed v_{A} and v_{B} respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be :$ (1) $1 : 1$ (2) $r_{A} : r_{B}$ (3) $v_{A} : v_{B}$ (4) $r_{B} : r_{A}$ 36. $A particle moves in a circle of radius 5 cm with constant speed and time period 0.2 πs. The acceleraiton of the particle is :$ (1) $15 m/ s^{2}$ (2) $25 m/ s^{2}$ (3) $36 m/ s^{2}$ (4) $5 m/ s^{2}$ 37. $A particle moves so that its position vector is given by r = cos ωt x + sin ωt y . Where, ω is a constant. Which of the following is true? [NEET 2016]$ (1) $Velocity and acceleration both are perpendicular to r.$ (2) $Velocity and acceleration both are parallel to r.$ (3) $Velocity is perpendicular to r and acceleration is directed towards the origin.$ (4) $Velocity is perpendicular to r and acceleration is directed away from the origin.$ 38. $The position ' x' of a particle varies with a time as x = a t^{2} - b t^{3} where ' a' and ' b' are constants. The acceleration of the particle will be zero at time ' t' is equal to$ (1) $\frac{2 a}{3 b}$ (2) $\frac{a}{b}$ (3) $\frac{a}{3 b}$ (4) $zero$ 39. $A particle moves around a circular path of radius ' r' with uniform speed ' V'. After moving half the circle, the average acceleration of the particle is$ (1) $\frac{V ^{2}}{r}$ (2) $\frac{2 V ^{2}}{r}$ (3) $\frac{2 V ^{2}}{πr}$ (4) $\frac{V ^{2}}{πr}$ 40. $A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the n^{th} power of R . If the period of rotation of the particle is T, then:$ (1) $Tα R^{(n + 1) /2}$ (2) $Tα R^{n /2}$ (3) $Tα R^{3/2} For any n.$ (4) $Tα R^{\frac{n}{2} + 1}$ 41. $Two stones of masses m and 2 m are whirled in horizontal circles the heavier one in radius \frac{r}{2} and the lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier stone when they experience same centripetal forces. The value of n is :$ (1) $3$ (2) $4$ (3) $1$ (4) $2$ 42. $Consider the motion of a particle described by x = acos t, y = asin t and z = t . The trajectory traced by the particle as a function of time is$ (1) $helix$ (2) $circular$ (3) $elliptical$ (4) $straight line$ 43. $A particle is moving with uniform speed along the circumference of a circle of radius R under the action of acentral fictitious force F which is inversely proportional to R^{3} . Its time period of revolution will be given by :$ (1) $T \propto R^{\frac{5}{2}}$ (2) $T \propto R^{2}$ (3) $T \propto R^{\frac{4}{3}}$ (4) $T \propto R^{\frac{3}{2}}$ 44. $Two objects are projected at an angle θ^{\circ} and (90 - θ)^{\circ}, to the horizontal with the same speed. The ratio of their maximum vertical heights is$ (1) $1 : tan θ$ (2) $1 : 1$ (3) $tan^{2} θ : 1$ (4) $tan θ : 1$ 45. $The position vector of a particle R as a function of time is given by: R = 4sin(2πt) i^+ 4cos(2πt) Where R is in meters, t is seconds and i^and j^denote unit vectors along x-and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?$ (1) $Magnitude of acceleration vector is \frac{v ^{2}}{R}, where v is the velocity of particle$ (2) $Magnitude of the velocity of particle is 8 meter/second$ (3) $path of the particle is a circle of radius 4 meter.$ (4) $Acceleration vector is along - R$ 46. $The point A moves with a uniform speed along the circumference of a circle of radius 0.36 m and cover 30^{\circ} in 0.1 s . The perpendicular projection ’ P ’ form ' A^{’} on the diameter MN represents the simple harmonic motion of ’ P ’ . The restoration force per unit mass when P touches M will be:$ (1) $100 N$ (2) $50 N$ (3) $9.87 N$ (4) $0.49 N$ 47. $A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of ' P' is such that it sweeps out a length s = t^{3} + 5, where s is in meters and t is in seconds. The radius of the path is 20 m. The acceleration of ' P' when t = 2 s is nearly.$ (1) $13 m / s^{2}$ (2) $12 m / s^{2}$ (3) $7.2 m / s^{2}$ (4) $14 m / s^{2}$ 48. $Two trains, which are moving along different tracks in opposite directions are put on the same track by mistake. On noticing the mistake, when the trains are 300 m apart the drivers.start slowing down the trains. The graphs given below show decrease in their velocities as function of time. The separation between the trains when both have stopped is$ (1) $120 m$ (2) $20 m$ (3) $60 m$ (4) $280 m$ 49. $A stone is dropped from a height of 100 m, while another one is projected vertically upwards from the ground with a velocity of 25 m / s at the same time.The time in seconds after which they will have the same height is (acceleration due to gravity, g = 10 ms^{- 1})$ (1) $4$ (2) $5$ (3) $6$ (4) $7$ 50. $The angular speed of a flywheel making 120 revolutions/minute is$ (1) $4 π r a d / s$ (2) $4 π^{2} r a d / s$ (3) $π r a d / s$ (4) $2 π r a d / s$ 51. $A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in radian/s) is:$ (1) $9$ (2) $18$ (3) $27$ (4) $36$ 52. $A block of mass 10 kg in contact against the inner wall of a hollow cylindrical drum of radius 1m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be (g = 10 m/ s^{2})$ (1) $10 π rad/s$ (2) $10 rad/s$ (3) $\frac{10}{2 π} rad/s$ (4) $10 rad/s$ 53. $A smooth wire of length 2 πr is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed ω about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of ω ² is equal to :$ (1) $\frac{3 g}{2 r}$ (2) $\frac{2 g}{( r 3 )}$ (3) $\frac{( g 3 )}{r}$ (4) $\frac{2 g}{r}$ 54. $Rain is falling at an angle of 30^{\circ} from the vertical due to the wind with a speed of 40 m / s . A car is travelling horizontally in the direction opposite to the wind, at a speed of 40 m / s . At what angle from the vertical will it experience the rain falling from?$ (1) $30^{\circ}$ (2) $60^{\circ}$ (3) $90^{\circ}$ (4) $120^{\circ}$ 55. $A body is moving with a uniform speed of 20 ms^{- 1} on a horizontal circle. The change in velocity of the body in half revolution is$ (1) $20 ms^{- 1}$ (2) $10 ms^{- 1}$ (3) $40 ms^{- 1}$ (4) $\frac{20}{2} ms^{- 1}$ 56. $A particle moves in a circle of radius 5 cm with constant speed and time period 0.2 π s . The acceleration of the particle is$ (1) $15 m / s^{2}$ (2) $25 m / s^{2}$ (3) $36 m / s^{2}$ (4) $5 m / s^{2}$ 57. $A particle starting from rest, moves in a circle of radius 'r'. It attains a velocity of V_{0} m/s in the n^{t h} round. Its angular acceleration will be:$ (1) $\frac{V _{o}}{n} rad/ s^{2}$ (2) $\frac{V _{o}^{2}}{2 π n r ^{2}} rad/ s^{2}$ (3) $\frac{V _{o}^{2}}{4 π n r ^{2}} rad/ s^{2}$ (4) $\frac{V _{o}^{2}}{4 π n r} rad/ s^{2}$ 58. $In the given figure, a = 15 m/ s^{2} represents the total acceleration of a particle moving in the clockwise direction in a circle of radius R = 2.5 m at a given instant of time. The speed of the particle is$ (1) $6.2 m/s$ (2) $4.5 m/s$ (3) $5.0 m/s$ (4) $5.7 m/s$ 59. $For a particle in uniform circular motion, the acceleration a at a point P (R, θ) on the circle of radius R is (Here θ is measured from the x -axis)$ (1) $- \frac{v ^{2}}{R} cos θ i + \frac{v ^{2}}{R} sin θ j$ (2) $- \frac{v ^{2}}{R} sin θ i + \frac{v ^{2}}{R} cos θ j$ (3) $- \frac{v ^{2}}{R} cos θ i - \frac{v ^{2}}{R} sin θ j$ (4) $\frac{v ^{2}}{R} i + \frac{v ^{2}}{R} j$ 60. $A ball rolls off the top of a stairway with horizontal velocity u . The steps are 0.1 m high and 0.1 m wide. The minimum velocity u with which that ball just hits the step 5 of the stairway will be x s^{- 1} where x =_______ [use g = 10 m / s^{2}].$