Kinematics PYQs Set 3 (PDF)

Set 3 of 14 · Questions 61-90 of 405

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Mere Teacher · Previous Year Questions JEE Main Physics · Kinematics · Set 3 (Q61-90)
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61. $A bus travelling the first one‐third distance at a speed of 10 k m / h, the next one‐third at 20 k m / h and at last one‐third at 60 k m / h . The average speed of the bus is$ (1) $9 k m / h$ (2) $16 k m / h$ (3) $18 k m / h$ (4) $48 k m / h .$ 62. $Two bodies of masses ' m_{1}' and ' m_{2}' are dropped from two different heights h_{1} and h_{2} respectively. The ratio of the times taken by the two masses to touch the ground is (neglect air resistance)$ (1) $\frac{h _{1}}{h _{2}}$ (2) $\frac{m _{1} h _{1}}{m _{2} h _{2}}$ (3) $\frac{m _{1} h _{2}}{m _{2} h _{1}}$ (4) $\frac{h _{1}}{h _{2}}$ 63. $Which of the following is not a vector quantity?$ (1) $Momentum$ (2) $Weight$ (3) $Potential energy$ (4) $Nuclear spin$ 64. $A particle is moving in xy -plane as x = (4 t + t^{2}) i, y = (2 t + \frac{t ^{2}}{2}) j where x & y are displacements measured along x and y axes respectively in meters and t in seconds. What is the velocity of the particle?$ (1) $v = (4 + t) i + (2 + t) j$ (2) $v = (4 + 2 t) i + (2 + t) \cdot j$ (3) $v = (4 + 2 t) i + (2 + \frac{t}{2}) j$ (4) $v = (4 + t) i + (2 + \frac{t}{2}) j$ 65. $Assertion (A) : The range of a projectile is maximum when the angle of projection is 45^{\circ} . Reason (R) : The range of a projectile depends only on the angle of projection.$ (1) $Both (A) and (R) are true and (R) is the correct explanation of (A).$ (2) $Both (A) and (R) are true but (R) is not the correct explanation of (A).$ (3) $(A) is true but (R) is false.$ (4) $(A) is false but (R) is true.$ 66. $A ball is thrown vertically upward from the ground at time, t = 0 s . It passes the top of a tower at t = 3 s and 2 s later is reaches and its maximum height. The height of the tower is (Acceleration due to gravity, g = 10 m / s^{2})$ (1) $105 m$ (2) $125 m$ (3) $85 m$ (4) $65 m$ 67. $A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 m s^{- 1} to 20 m s^{- 1} while passing through adistance 135 m in t second. The value of t is$ (1) $12$ (2) $9$ (3) $10$ (4) $1.8$ 68. $The correct position (x) - time (t) graph for a particle moving with negative acceleration is$ (1) (2) (3) (4) 69. $Given below are two statements: Statement I: A truck and a car moving with same kinetic energy are brought to rest by applying breaks which provide equal retarding forces. Both come to rest in equal distance. Statement II: A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero. In the light of given statements, choose the most appropriate answer from the options given below$ (1) $Statement I is correct but statement II is incorrect$ (2) $Statement I is incorrect but statement II is correct$ (3) $Both statement I and Statement II are correct$ (4) $Both statement I and statement II are incorrect$ 70. $A particle starts from origin at time t = 0 and moves in positive x -direction. Its velocity v varies with times as v = 10 t i cm / s . The distance covered by the particle in 8 s will be$ (1) $320 cm$ (2) $80 cm$ (3) $120 cm$ (4) $640 cm$ 71. $y = (Pt^{2} - Q t^{3}) m is the vertical displacement of a ball which is moving in vertical plane. Then the maximum height that the ball can reach is$ (1) $\frac{27 P ^{3}}{4 Q ^{2}}$ (2) $\frac{4 Q ^{2}}{27 P ^{3}}$ (3) $\frac{4 P ^{3}}{27 Q ^{2}}$ (4) $\frac{27 Q ^{2}}{4 P ^{3}}$ 72. $The position vector of a particle R as a function of time is given by R = 4 sin (2 πt) i + 4 cos (2 πt) j where R is in metre, t is in seconds and i and j denote unit vectors along x and y -directions, respectively. Which one of the following statements is wrong for the motion of particle?$ (1) $Acceleration is along - R$ (2) $Magnitude of acceleration vector is \frac{v ^{2}}{R}, where v is the velocity of particle$ (3) $Magnitude of the velocity of particle is 8 m / s$ (4) $Path of the particle is a circle of radius 4 m$ 73. $A particle moves over an xy -plane with a constant acceleration a = (4 i + 4 j) m / s^{2} . At time t = 0, the velocity is (4 i) m / s^{2} . The speed of the particle when it is displaced by 6.0 m parallel to the X -axis is$ (1) $45 m / s$ (2) $60 m / s$ (3) $310 m / s$ (4) $20 m / s$ 74. $Which of the following is not true about vectors A, B and C ?$ (1) $(A \cdot A) (B \cdot C) is a scalar value.$ (2) $(A \times B) \cdot (B \times C) is a scalar value.$ (3) $(A \times C) \times (B \times C) is a scalar value.$ (4) $A \times (B \times C) is a vector value.$ 75. $The angle of projection for a projectile to have same horizontal range and maximum height is :$ (1) $tan^{- 1} (4)$ (2) $tan^{- 1} (\frac{1}{4})$ (3) $tan^{- 1} (\frac{1}{2})$ (4) $tan^{- 1} (2)$ 76. $A ball is throw at a speed of 20 m / s at an angle of 30^{\circ} with the horizontal. The maximum height reached by the ball is (Use g = 10 m / s^{2})$ (1) $2 m$ (2) $3 m$ (3) $4 m$ (4) $5 m$ 77. $A particle is in uniform circular motion. Related to one complete revolution of the particle, which among the statements is incorrect?$ (1) $Average acceleration of the particle is zero.$ (2) $Displacement of the particle is zero.$ (3) $Average speed of the particle is zero.$ (4) $Average velocity of the particle is zero.$ 78. $At time t = 0 a particle starts travelling from a height 7 z^c m in a plane keeping z coordinate constant. At any instant of time it's position along the x and y directions are defined as 3t and 5 t^{3} respectively. At t = 1s acceleration of the particle will be$ (1) $-30y$ (2) $30y$ (3) $3x + 15y$ (4) $3x + 15y+7z$ 79. $The ratio of the distances travelled by a freely falling body in the 1st, 2nd, 3rd and 4th second [NEET 2022]$ (1) $1 : 4 : 9 : 16$ (2) $1 : 3 : 5 : 7$ (3) $1 : 1 : 1 : 1$ (4) $1 : 2 : 3 : 4$ 80. $Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t_{1} . On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t_{2} . The time taken by her to walk up on the moving escalator will be [NEET 2017]$ (1) $\frac{t _{1} + t _{2}}{2}$ (2) $\frac{t _{1} t _{2}}{t _{2} - t _{1}}$ (3) $\frac{t _{1} t _{2}}{t _{2} + t _{1}}$ (4) $t_{1} - t_{2}$ 81. $The ranges and heights for two projectiles projected with the same initial velocity at angles 4 2^{0} and 4 8^{0} with the horizontal are R_{1}, R_{2} and H_{1}, H_{2}, respectively. Choose the correct option :$ (1) $R_{1} > R_{2} and H_{1} = H_{2}$ (2) $R_{1} = R_{2} and H_{1} < H_{2}$ (3) $R_{1} < R_{2} and H_{1} < H_{2}$ (4) $R_{1} = R_{2} and H_{1} = H_{2}$ 82. $A projectile is given an initial velocity - (3 i + 4 j) m / s where, ı is along the ground and ȷ is along the vertical. Assuming g = 10 m / s^{2}, if the equation of its trajectory can be written as \frac{1}{9} (βx + γ x^{2}), then the value of γ is$ (1) $-8$ (2) $-5$ (3) $-6$ (4) $-12$ 83. $A toy cart is tied to the end of an unstretched string of length ' l'. When revolved, the toy cart moves in horizontal circle with radius ' 2 l' and time period T . If it is speeded until it moves in horizontal circle of radius ' 3 l with period T_{1}, relation between T and T_{1} is (Hooke's law is obeyed)$ (1) $T_{1} = \frac{2}{3} T$ (2) $T_{1} = \frac{3}{2} T$ (3) $T_{1} = \frac{2}{3} T$ (4) $T_{1} = \frac{3}{2} T$ 84. $The position of a particle as a function of time t, is given by x (t) = at + b t^{2} - c t^{3} where, a, b and c are constants. When the particle attains zero acceleration, then its velocity will be:$ (1) $a + \frac{b ^{2}}{4 c}$ (2) $a + \frac{b ^{2}}{3 c}$ (3) $a + \frac{b ^{2}}{c}$ (4) $a + \frac{b ^{2}}{2 c}$ 85. $A particle moves along a straight line such that its displacement ' x' varies with time ' t' as x = α t^{3} + β t^{2} + γ, where α, β, γ are constants. V_{1} is the average velocity of the particle during its journey between t = 1 s and t = 3 s . V_{2} is the instantaneous velocity of the particle at t = 3 s . The ratio \frac{V _{1}}{V _{2}} is$ (1) $\frac{27 α + 9 β}{26 α + 6 β}$ (2) $\frac{9 α + 3 β}{18 α + 4 β}$ (3) $\frac{13 α + 4 β}{27 α + 6 β}$ (4) $\frac{26 α + 8 β}{9 α + 3 β}$ 86. $Find the angle between the two vectors a = 3 i + 2 j + 5 k, b = 5 i + 3 j + k .$ (1) $cos^{- 1} (\frac{26}{1330})$ (2) $sin^{- 1} (\frac{26}{1330})$ (3) $cos^{- 1} (\frac{26}{1335})$ (4) $tan^{- 1} (\frac{26}{1330})$ 87. $The velocity (v) of a particle starting from rest increases linearly withtime (t) as v = 4 t, where v is in ms^{- 1} and t is in second. The distance covered by the particle in the first 4 seconds is$ (1) $16 m$ (2) $32 m$ (3) $8 m$ (4) $64 m$ 88. $The position, velocity and acceleration of a particle moving with a constant acceleration can be representedby:$ (1) (2) (3) (4) 89. $Which of the following curve does not represent motion in one dimension?$ (1) (2) (3) (4) 90. $A particle moves in a straight line so that its displacement x at any time t is given by x^{2} = 1 + t^{2} . Its acceleration at any time t is x^{- n} where n =_______$