Circular Motion PYQs Set 3 (PDF)

Set 3 of 3 · Questions 61-86 of 86

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Mere Teacher · Previous Year Questions NEET Physics · Circular Motion · Set 3 (Q61-86)
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61. $A particle is moving along a circular path with a constant speed of 10 m s^{- 1} . What is the magnitude of the change in velocity of the particle, when it moves through an angle of 60° around the centre of the circle?$ (1) $103 m / s$ (2) $zero$ (3) $102 m / s$ (4) $10 m / s$ 62. $A body is whirled in a horizontal circle of radius 20 cm. It has an angular velocity of 10 r a d / s . What is its linear velocity at any point on circular path?$ (1) $20 m / s$ (2) $2 m / s$ (3) $10 m / s$ (4) $2 m / s .$ 63. $Two bullets are fired horizontally and simultaneously towards each other from roof tops of two buildings 100 m apart and of same height of 200 m, with the same velocity of 25 m/s. When and where will the two bullets collide? (g = 10 m/ s^{2})$ (1) $after 2s at a height of 180 m$ (2) $after 2s at a height of 20 m$ (3) $after 4s at a height of 120 m$ (4) $they will not collide$ 64. $A wire, which passes through the hole is a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is$ (1) $always radially outwards$ (2) $always radially inwards$ (3) $radially outwards initially and radially inwards later$ (4) $radially inwards initially and radially outwards later.$ 65. $A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is 8 m / s . The speed of the particle on the rim of the wheel at the same level as the centre of wheel, will be:$ (1) $42 m / s$ (2) $8 m / s$ (3) $4 m / s$ (4) $82 m / s$ 66. $A particle is moving on circular path as shown in the figure. Then displacement from P_{1} to P_{2} is$ (1) $2 r cos \frac{θ}{2}$ (2) $2 r tan \frac{θ}{2}$ (3) $2 r sin θ$ (4) $2 r sin \frac{θ}{2}$ 67. $A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :$ (1) $hyperbola$ (2) $parabola in the direction of motion of plane$ (3) $straight line vertically down the plane$ (4) $parabola in a direction opposite to the motion of plane$ 68. $The x and y coordinates of the particle at any time are x = 5 t - 2 t^{2} and y = 10 t respectively where x and y are in metres and t in seconds. The acceleration of the particle at t = 2 s is$ (1) $5 m s^{- 2}$ (2) $- 4 m s^{- 2}$ (3) $- 8 m s^{- 2}$ (4) $0$ 69. $A bus is moving on a straight road towards north with a uniform speed of 50 km/hour then it turns left through 9 0^{0} . If the speed remains unchanged after turning, the increase in the velocity of bus in the turning process is$ (1) $70.7 k m / h r along south‐west direction$ (2) $zero$ (3) $50 k m / h r along west$ (4) $70.7 k m / h r along north‐west direction$ 70. $The surface of a hill inclined at an angle 30^{\circ} to the horizontal. A stone is thrown from the summit of the hill (point A) at an initial speed 10 m / s at angle 60^{\circ} to the vertical. If the stone strikes the hill at point B as shown in the figure, the distance between A and B is (Take g = 10 m / s^{2})$ (1) $10 m$ (2) $15 m$ (3) $20 m$ (4) $30 m$ 71. $A particle moves in x‐y plane according to rule x = a s inω t and y = a cos ω t . The particle follows$ (1) $an elliptical path$ (2) $a circular path$ (3) $a parabolic path$ (4) $a straight-line path inclined equally to x and y ‐axes$ 72. $Rain is falling vertically with a speed of 30 m / s . A man rides a bicycle with a speed of 10 m / s from East to West direction. At what the angle with the vertical, he sees the rain falling?$ (1) $tan^{- 1} (\frac{1}{3}) towards west$ (2) $tan^{- 1} (3) towards west$ (3) $tan^{- 1} (\frac{1}{3}) towards east$ (4) $tan^{- 1} (3) towards east$ 73. $A man running at a speed of 5 km / h, find that the rain falls vertically. When he stops running, he finds that the rain is falling at an angle of 60^{\circ} with the horizontal. The velocity of rain with respect to running man is$ (1) $\frac{5}{3} km / h$ (2) $\frac{5 3}{2} km / h$ (3) $\frac{4 3}{2} km / h$ (4) $53 km / h$ 74. $A sportsman runs around a circular track of radius r such that he traverses the path ABAB . The distance travelled and displacement, respectively, are$ (1) $πr, 3 r$ (2) $2 r, 3 πr$ (3) $3 πr, 2 r$ (4) $3 πr, πr$ 75. $Rain is falling vertically with a speed of 12 m s^{- 1} . A woman rides a bicycle with a speed of 12 m s^{- 1} in east to west direction. What is the direction in which she should hold her umbrella?$ (1) $30^{\circ} towards West$ (2) $45^{\circ} towards West$ (3) $30^{\circ} towards East$ (4) $45^{\circ} towards East$ 76. $When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees that rain drops are coming at an angle 60^{\circ} from the horizontal. On further increasing the speed of the car to (1 + β) v this angle changes to 45^{\circ} The value of β is close$ (1) $0.37$ (2) $0.41$ (3) $0.73$ (4) $0.5$ 77. $A wheel starting from rest gains an angular velocity of 10 rad s^{- 1} after uniformly accelerated for 5 sec . The total angle through which it has turned is$ (1) $25 π rad$ (2) $50 π rad$ (3) $25 rad$ (4) $100 rad$ 78. $The acceleration of a vertically projected body at its highest reaching position is$ (1) $0$ (2) $Equal to acceleration due to gravity at the place$ (3) $Infinity$ (4) $- 1 ms^{- 2}$ 79. $A balloon is moving up in air vertically above a point A on the ground. When it is at a height h_{1} a girl standing at a distance d (point B) from A (see figure) sees it at an angle 45^{\circ} with respect to the vertical. When the balloon climbs up a further height h_{2} it is seen at an angle 60^{o} with respect to the vertical if the girl moves further by a distance 2.464 d (point ). Then the height h_{2} is (given tan 30^{\circ} = 0.5774)$ (1) $d$ (2) $0.732 d$ (3) $1.464 d$ (4) $0.464 d$ 80. $Two particles having mass M and m are moving in a circular path having radius R and r. If their time period are same then the ratio of angular velocity will be$ (1) $\frac{r}{R}$ (2) $\frac{R}{r}$ (3) $1$ (4) $\frac{R}{r} .$ 81. $In the given figure, a = 1 5 m s^{-2} represents the total acceleration of a particle moving in the clockwise direction in a circle of radius R = 2.5 m at a given instant of time. The speed of the particle is$ (1) $4.5 m s^{- 1}$ (2) $5.0 m s^{- 1}$ (3) $5.7 m s^{- 1}$ (4) $6.2 m s^{- 1}$ 82. $Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed ω . The disc are in the same horizontal plane. At time t = 0, the points P and Q are facing each other as shown in the figure. The relative speed between the two points P and Q is v_{r} . as function of times best represented by$ (1) (2) (3) (4) 83. $A string of length ' L' fixed at one end carries a body of mass ' m' at the other end. The mass is revolved in a circle in the horizontal plane about a vertical axis passing through the fixed end of the string. The string makes angle ' θ' with the vertical. The angular frequency of the body is ' ω'. The tension in the string is$ (1) $m L^{2} ω$ (2) $m L ω^{2}$ (3) $\frac{ω ^{2}}{m L}$ (4) $\frac{m ω ^{2}}{L}$ 84. $The angle between velocity and acceletation of a particle describing uniform circular motion is$ (1) $180^{\circ}$ (2) $45^{\circ}$ (3) $90^{\circ}$ (4) $60^{\circ}$ 85. $A particle of mass ' m' is moving in circular path of constant radius ' r' such that centripetal acceleration is varying with time ' t' as K^{2} r t^{2} where K is a constant. The power delivered to the particle by the force acting on it is$ (1) $m^{2} K^{2} r^{2} t^{2}$ (2) $m K^{2} r^{2} t$ (3) $m K^{2} r t^{2}$ (4) $mK r^{2} t$ 86. $A particle moves along a circle of radius (\frac{20}{π}) m with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begun, the tangential acceleration is$ (1) $40 m/s^{2}$ (2) $640 π m/s^{2}$ (3) $160 π m/s^{2}$ (4) $40 π m/s^{2}$