Work, Energy & Power PYQs Set 3 (PDF)

Set 3 of 10 · Questions 61-90 of 294

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Mere Teacher · Previous Year Questions JEE Main Physics · Work, Energy & Power · Set 3 (Q61-90)
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61. $A car of mass m starts from rest and acceleratesso that the instantaneous power delivered tothe car has a constant magnitude P_{0} . Theinstantaneous velocity of this car is proportional to (Mains 2012)$ (1) $t^{2} P_{0}$ (2) $t^{\frac{1}{2}}$ (3) $t^{- 1/2}$ (4) $\frac{t}{m}$ 62. $A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to:$ (1) $t$ (2) $t^{3/2}$ (3) $t^{2}$ (4) $t^{2/3}$ 63. $A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of 20 ms^{- 1} . The ball gets deflected by anobstacle on the way. After deflection it moves with 5 % of its initial kinetic energy. What is the speed of the ball now?$ (1) $19.0 ms^{- 1}$ (2) $4.47 ms^{- 1}$ (3) $14.41 ms^{- 1}$ (4) $1.00 ms^{- 1}$ 64. $A body is moved along a straight line by an engine which delivers a constant power. The distance moved by the body in time 't' is proportional to$ (1) $t^{1/2}$ (2) $t^{3/4}$ (3) $t^{3/2}$ (4) $t^{2}$ 65. $A force F = 20 + 10 y acts on a particle in y -direction, where F is in newton and y in metre. Work done by this force to move the particle from y = 0 to y = 1 m is [NEET 2019]$ (1) $5 J$ (2) $25 J$ (3) $20 J$ (4) $30 J$ 66. $A block of mass 10 kg, moving in x direction with a constant speed of 10 m s^{- 1}, is subjectedto a retarding force F = 0.1 xJ / m during its travel from x = 20 m to 30 m . Its final KE will be$ (1) $275 J$ (2) $250 J$ (3) $475 J$ (4) $450 J$ 67. $A stationary particle explodes into two particles of masses m_{1} and m_{2} which move in opposite directions with velocities v_{1} and v_{2} . The ratio of their kinetic energies E_{1} / E_{2} is$ (1) $m_{2} / m_{1}$ (2) $m_{1} / m_{2}$ (3) $1$ (4) $m_{1} v_{2} / m_{2} v_{1}$ 68. $A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has force constant value k . The mass is released from rest with the springinitially unstretched. The maximum extension produced in the length of the spring will be$ (1) $2 Mg / k$ (2) $4 Mg / k$ (3) $Mg /2 k$ (4) $Mg / k$ 69. $An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?$ (1) $m v^{3}$ (2) $\frac{1}{2} m v^{2}$ (3) $\frac{1}{2} m^{2} v^{2}$ (4) $\frac{1}{2} m v^{3}$ 70. $A body of mass 8 kg, under the action of a force, is displaced according to the equation, s = \frac{t ^{2}}{4} m, where t is the time. Find the work done by the force in the first 4 s .$ (1) $9 J$ (2) $16 J$ (3) $6 J$ (4) $3 J$ 71. $The ratio of specific heats (\frac{C _{P}}{C _{V}}) in terms of degree of freedom (f) is given by:$ (1) $(1 + \frac{f}{3})$ (2) $(1 + \frac{2}{f})$ (3) $(1 + \frac{f}{2})$ (4) $(1 + \frac{1}{f})$ 72. $A child is sitting on a swing. Its minimum and maximum heights from the ground 0.75 m and 2 m respectively, its maximum speed will be$ (1) $10 m / s$ (2) $5 m / s$ (3) $8 m / s$ (4) $15 m / s .$ 73. $If a body has a potential energy of (4 x^{2} + 2 x) J at a height of 2 m, then the force acting on the body is$ (1) $9 N$ (2) $27 N$ (3) $18 N$ (4) $0 N$ 74. $The potential energy between two atoms, in a molecule, is given by U (x) = \frac{a}{x ^{12}} - \frac{b}{x ^{6}} where a and b are positive constants and x is the distance between the atoms. The atom is in stable equilibrium, when$ (1) $x = (\frac{2 a}{b})^{1/6}$ (2) $x = (\frac{11 a}{5 b})^{1/6}$ (3) $x = 0$ (4) $x = (\frac{a}{2 b})^{1/6}$ 75. $A force acts on a 2 kg object so that its position is given as a function of time as x = 3 t^{2} + 5. What is the work done by this force in first 5 seconds?$ (1) $850 J$ (2) $900 J$ (3) $875 J$ (4) $950 J$ 76. $Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :$ (1) $3 : 5$ (2) $5 : 4$ (3) $2 : 5$ (4) $4 : 5$ 77. $A body of mass m = 1 0^{-2} kg is moving in a medium and experiences a frictional force F = - k v^{2} . Its initial speed is v_{0} = 10 m s^{-1} . If after 10 s, its energy is \frac{1}{8} m v_{0}^{2},the value of k will be:$ (1) $1 0^{-1} Kg m^{-1} s^{-1}$ (2) $1 0^{-3} Kg m^{-1}$ (3) $1 0^{-3} Kg s^{-1}$ (4) $1 0^{-4} Kg m^{-1}$ 78. $A particle of mass m_{1} is moving with a velocity v_{1} and another particle of mass m_{2} is moving with a velocity v_{2} . Both of them have the same momentum but their different kinetic energies are E_{1} and E_{2} respectively. If m_{1} > m_{2} then$ (1) $E_{1} < E_{2}$ (2) $\frac{E _{1}}{E _{2}} = \frac{m _{1}}{m _{2}}$ (3) $E_{1} > E_{2}$ (4) $E_{1} = E_{2}$ 79. $If the Kinetic energy of a moving body becomes four times its initial Kinetic energy, then the percentage change in its momentum will be:$ (1) $100%$ (2) $200%$ (3) $300%$ (4) $400%$ 80. $The height of Victoria falls is 63m. What is the difference in temperature of water at the top and at the bottom of fall? [Given 1cal=4.2J and specific heat of water = 1 c a l g^{- 10} C^{- 1}]$ (1) $0. 14 7^{0} C$ (2) $14. 7 6^{0} C$ (3) $1. 47 6^{0} C$ (4) $0. 01 4^{0} C$ 81. $A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is$ (1) $40 m s^{- 1}$ (2) $120 m s^{- 1}$ (3) $100 m s^{- 1}$ (4) $80 m s^{- 1}$ 82. $The potential energy of particle in a force field is U = \frac{A}{r ^{2}} - \frac{B}{r}, where A and B are positive constants and r si the distance of particle from the center of the field. For stable equilibrium, the distance of the particle is:$ (1) $B / 2A$ (2) $2A / B$ (3) $A / B$ (4) $B / A$ 83. $A motor boat is moving in a river with velocity v = 7 i + 2 j - 5 k ms^{- 1} . If the flow of water offers resistive force F = 9 i + 3 j - 3 k N, then the power of the boat is$ (1) $13 W$ (2) $69 W$ (3) $12 W$ (4) $84 W$ 84. $A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation s = \frac{1}{3} t^{2} ’ where t is in seconds. Work done by the force in 2 seconds is$ (1) $\frac{19}{5} J$ (2) $\frac{5}{19} J$ (3) $\frac{3}{8} J$ (4) $\frac{8}{3} J.$ 85. $A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight-line. The distance moved by the box in time ’ t ’ is proportional to:-$ (1) $t^{2/3}$ (2) $t^{3/2}$ (3) $t$ (4) $t^{1/2}$ 86. $A body of mass 5 kg is thrown vertically up with a kinetic energy of 490 J . The height at which the kinetic energy of the body becomes half of the original value is$ (1) $5 m$ (2) $2.5 m$ (3) $10 m$ (4) $12.5 m$ 87. $A 12 kg bomb at rest explodes into two pieces of 4 kg and 8 kg . If the momentum of 4 kg piece is 20 N s, the kinetic energy of the 8 kg piece is$ (1) $25 J$ (2) $20 J$ (3) $50 J$ (4) $40 J$ 88. $An object is moving in a straight line under the influence of a source of constant power. If v and t are velocity and time respectively, then$ (1) $v \propto t^{2}$ (2) $v \propto t^{1/2}$ (3) $v \propto t$ (4) $v \propto t^{3/2}$ 89. $Sun light falls normally on a surface of area 36 c m^{2} and exerts an average force of 7. 2 x 1 0^{- 9} N within a time period of 20 minutes. Considering a case of complete absorption, the energy flux of incident light is$ (1) $25. 92 x 1 0^{2} W/ c m^{2}$ (2) $8. 64 x 1 0^{- 6} W/ c m^{2}$ (3) $6.0 W/ c m^{2}$ (4) $0.06 W/ c m^{2}$ 90. $A body of mass 2 kg thrown vertically from the ground with a velocity of 8 ms^{- 1} reaches a maximum height of 3 m . The work done by the air resistance is (acceleration due to gravity = 10 ms^{- 2})$ (1) $4 J$ (2) $60 J$ (3) $64 J$ (4) $8 J$