STD 11 - Newtons laws of motion PYQs: JEE Mains Physics – Page 2

Showing 51–100 of 114 questions

51. 51. At any instant the velocity of a particle of mass \(500\,g\) is \(\left(2 t \hat{ i }+3 t ^2 \hat{ j }\right)\,ms ^{-1}\). If the force acting on the particle at \(t=1 s\) is \((\hat{i}+x \hat{j}) N\). Then the value of \(x\) will be: 2023 Medium
52. 52. Figures \((a), (b), (c)\) and \((d)\) show variation of force with time. The impulse is highest in figure.
    2023 Medium
53. 53. Force acts for \(20\,s\) on a body of mass \(20\,kg\), starting from rest, after which the force ceases and then body describes \(50\,m\) in the next \(10\,s\). The value of force will be \(..........\,N\) 2023 Medium
54. 54. Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R.\) Assertion \(A:\) An electric fan continues to rotate for some time after the current is switched off. Reason \(R:\) Fan continuous to rotate due to inertia of motion. In the light of above statements, choose the most appropriate answer from the options given below. 2023 Medium
55. 55. Given below are two statements: Statement\(-I :\) An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable. Statement\(-II :\) Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed. In the light of the above statements, choose the correct answer from the options given below : 2023 Medium
56. 56. The figure represents the momentum time \((p-t)\) curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum respectively ? If \(\left(t_3-t_2\right) < t_1\)
    2023 Medium
57. 57. The position vector of a particle related to time \(t\) is given by \(\overrightarrow{ r }=\left(10 t \hat{ i }+15 t ^2 \hat{ j }+7 \hat{ k }\right) m\) The direction of net force experienced by the particle is 2023 Medium
58. 58. Three force \(F_1=10\,N , F_2=8\,N , F _3=6\,N\) are acting on a particle of mass \(5\,kg\). The forces \(F _2\) and \(F _3\) are applied perpendicular so that particle remains at rest. If the force \(F_1\) is removed, then the acceleration of the particle is \(......ms^{-2}\) 2023 Medium
59. 59. A balloon has mass of \(10\,g\) in air. The air escapes from the balloon at a uniform rate with velocity \(4.5\,cm / s\). If the balloon shrinks in \(5\,s\) completely. Then, the average force acting on that balloon will be (in dyne). 2022 Easy
60. 60. A batsman hits back a ball of mass \(0.4 \; kg\) straight in the direction of the bowler without changing its initial speed of \(15 \; ms ^{-1}\). The impulse imparted to the ball is \(\dots \; Ns\) 2022 Easy
61. 61. A block '\(A\)' takes \(2\,s\) to slide down a frictionless incline of \(30^{\circ}\) and length ' \(l\) ', kept inside a lift going up with uniform velocity ' \(v\) '. If the incline is changed to \(45^{\circ}\), the time taken by the block, to slide down the incline, will be approximately \(........\,s\) 2022 Medium
62. 62. A block of mass \(200\, g\) is kept stationary on a smooth inclined plane by applying a minimum horizontal force \(F =\sqrt{ x }N\) as shown in figure. The value of \(x =.....\)
    2022 Medium
63. 63. A block of mass \(M\) placed inside a box descends vertically with acceleration \('a'\). The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of \('a'\) will be ............. 2022 Easy
64. 64. A block of metal weighing \(2 \,kg\) is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of \(1 \,kgs ^{-1}\) and at a speed of \(10 \,ms ^{-1}\). Then, the initial acceleration of the block, in \(ms ^{-2}\), will be .................
    2022 Medium
65. 65. A body of mass \(10 kg\) is projected at an angle of \(45^{\circ}\) with the horizontal. The trajectory of the body is observed to pass through a point \((20,10)\). If \(T\) is the time of flight, then its momentum vector, at time \(t =\frac{ T }{\sqrt{2}}\), is. \(\left[\right.\) Take \(\left.g=10 m / s ^{2}\right]\) 2022 Hard
66. 66. A body of mass \(M\) at rest explodes into three pieces, in the ratio of masses \(1: 1: 2\). Two smaller pieces fly off perpendicular to each other with velocities of \(30 \,ms ^{-1}\) and \(40 \,ms ^{-1}\) respectively. The velocity of the third piece will be ............... \(\,ms ^{-1}\) 2022 Medium
67. 67. A force on an object of mass \(100\, g\) is \((10 \hat{i}+5 \hat{j}) N\). The position of that object at \(t=\) \(2 s\) is \((a \hat{i}+b \hat{j}) m\) after starting from rest. The value of \(\frac{a}{b}\) will be.......... 2022 Medium
68. 68. A hanging mass \(M\) is connected to a four times bigger mass by using a string-pulley arrangement. as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by \(2\,Mg\) force. In this situation. tension in the string is \(\frac{x}{5}\) \(Mg\) for \(x =\) Neglect mass of the string and friction of the block (bigger mass) with ice slab. (Given \(g=\) acceleration due to gravity)
    2022 Medium
69. 69. A man of \(60\,kg\) is running on the road and suddenly jumps into a stationary trolly car of mass \(120\,kg\). Then. the trolly car starts moving with velocity \(2\,ms ^{-1}\). The velocity of the running man was _________\(ms ^{-1}\). when he jumps into the car 2022 Medium
70. 70. A mass of \(10 \,kg\) is suspended vertically by a rope of length \(5 \,m\) from the roof. A force of \(30 \,N\) is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is \(\theta=\tan ^{-1}\left(x \times 10^{-1}\right)\). The value of \(x\) is ................ \(\text { (Given } g =10 \,m / s ^{2} \text { ) }\) 2022 Medium
71. 71. A monkey of mass \(50\,kg\) climbs on a rope which can withstand the tension \((T)\) of \(350\,N\). If monkey initially climbs down with an acceleration of \(4\,m / s ^{2}\) and then climbs up with an acceleration of \(5\,m / s ^{2}\). Choose the correct option \(\left( g =10\,m / s ^{2}\right)\) 2022 Medium
72. 72. A person is standing in an elevator. In which situation, he experiences weight loss? 2022 Medium
73. 73. A uniform metal chain of mass \(m\) and length ' \(L\) ' passes over a massless and frictionless pulley. It is released from rest with a part of its length ' \(l\) ' is hanging on one side and rest of its length ' \(L -l\) ' is hanging on the other side of the pulley. At a certain point of time, when \(l=\frac{L}{x}\), the acceleration of the chain is \(\frac{g}{2}\). The value of \(x\) is ........
    2022 Hard
74. 74. An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero? 2022 Medium
75. 75. An object of mass \(5\, kg\) is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of \(10\, N\) throughout the motion. The ratio of time of ascent to the time of descent will be equal to \(\left[\right.\)Use \(g =10 \,ms ^{-2}]\) 2022 Hard
76. 76. For a free body diagram shown in the figure, the four forces are applied in the ' \(x\) ' and ' \(y\) ' directions. What additional force must be applied and at what angle with positive \(x\)-axis so that the net acceleration of body is zero?
    2022 Medium
77. 77. In the arrangement shown in figure \(a _{1}, a _{2}, a _{3}\) and \(a _{4}\) are the accelerations of masses \(m _{1}, m _{2}, m _{3}\) and \(m _{4}\) respectively. Which of the following relation is true for this arrangement?
    2022 Hard
78. 78. In two different experiments, an object of mass \(5\; kg\) moving with a speed of \(25\; ms ^{-1}\) hits two different walls and comes to rest within \((i)\) \(3\) second, \((ii)\) \(5\) seconds, respectively. Choose the correct option out of the following : 2022 Medium
79. 79. One end of a massless spring of spring constant \(k\) and natural length \(l_{0}\) is fixed while the other end is connected to a small object of mass \(m\) lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity \(\omega\) about an axis passing through fixed end, then the elongation of the spring will be 2022 Medium
80. 80. Three masses \(M =100\,kg , m _{1}=10\,kg\) and \(m_{2}=20\,kg\) are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. \(A\) force \(F\) is applied on the system so that the mass \(m_{2}\) moves upward with an acceleration of \(2\,ms ^{-2}\). The value of \(F\) is \(......N\) \(\left(\right.\) Take \(\left.g =10\,ms ^{-2}\right)\)
    2022 Hard
81. 81. Two billiard balls of mass \(0.05\,kg\) each moving in opposite directions with \(10\,ms ^{-1}\) collide and rebound with the same speed. If the time duration of contact is \(t=0.005\,s\), then \(\dots N\)is the force exerted on the ball due to each other. 2022 Medium
82. 82. Two bodies of masses \(m_{1}=5\,kg\) and \(m _{2}=3\,kg\) are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass \(m _{1}\) will be\(....N\) [Take \(g=10\,ms ^{-2}\) ]
    2022 Hard
83. 83. Two masses \(M _{1}\) and \(M _{2}\) are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass \(M _{2}\) is twice that of \(M_{1}\). the acceleration of the system is \(a_{1}\). When the mass \(M_{2}\) is thrice that of \(M_{1}\). The acceleration of The system is \(a_{2}\). The ratio \(\frac{a_{1}}{a_{2}}\) will be.
    2022 Medium
84. 84. A ball will a speed of \(9\, m / s\) collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of \(30^{\circ}\) with the original direction. The ratio of velocities of the balls after collision is \(x : y\) where \(x\) is........ 2021 Hard
85. 85. A block of mass \(m\) slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is : Given \({m}=8 \,{kg}, {M}=16\, {kg}\) Assume all the surfaces shown in the figure to be frictionless.
    2021 Hard
86. 86. A body of mass \(2\, kg\) moves under a force of \((2 \hat{ i }+3 \hat{ j }+5 \hat{ k }) \,N\). It starts from rest and was at the origin initially. After \(4 \,s\), its new coordinates are \((8, b, 20)\). The value of \(b\) is ........ . (Round off to the Nearest Integer) 2021 Medium
87. 87. A boy pushes a box of mass \(2\, kg\) with a force \(\overrightarrow{ F }=(20 \hat{ i }+10 \hat{ j }) N\) on a frictionless surface. If the box was initially at rest, then ...........  \(m\) is displacement along the \(x-\)axis after \(10\, s\). 2021 Medium
88. 88. A bullet of \('4\,g'\) mass is fired from a gun of mass \(4 \,{kg}\). If the bullet moves with the muzzle speed of \(50\, {ms}^{-1}\), the impulse imparted to the gun and velocity of recoil of gun are : 2021 Medium
89. 89. A bullet of mass \(0.1\, kg\) is fired on a wooden block to pierce through it, but it stops after moving a distance of \(50\, cm\) into it. If the velocity of bullet before hitting the wood is \(10\) \(m / s\) and it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is \('x' N.\) The value of \('x'\) to the nearest integer is................. \(N\) 2021 Medium
90. 90. A force \(\vec{F}=(40 \hat{i}+10 \hat{j})\, N\) acts on a body of mass \(5\, {kg}\). If the body starts from rest, its position vector \(\vec{r}\) at time \(t=10\, {s}\), will be - 2021 Medium
91. 91. A particle of mass \(M\) originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation \(F=F_{0}\left(1-\left(\frac{t-T}{T}\right)^{2}\right)\) Where \(F_{0}\) and \(T\) are constants. The force acts only for the time internal \(2 T\). The velocity \(v\) of the particle after time \(2 {T}\) is - 2021 Hard
92. 92. A person standing on a spring balance inside a stationary lift measures \(60 \,kg\). The weight of that person if the lift descends with uniform downward acceleration of \(1.8\, m / s ^{2}\) will be \(_{-} N\). \(\left[ g =10\, m / s ^{2}\right]\) 2021 Medium
93. 93. Consider a frame that is made up of two thin massless rods \(AB\) and \(AC\) as shown in the figure. \(A\) vertical force \(\overrightarrow{ P }\) of magnitude \(100 \;N\) is applied at point \(A\) of the frame. Suppose the force is \(\overrightarrow{ P }\) resolved parallel to the arms \(AB\) and \(AC\) of the frame. The magnitude of the resolved component along the arm \(AC\) is \(xN\). The value of \(x\), to the nearest integer, is ............ [Given : \(\sin \left(35^{\circ}\right)=0.573, \cos \left(35^{\circ}\right)=0.819\) \(\left.\sin \left(110^{\circ}\right)=0.939, \cos \left(110^{\circ}\right)=-0.342\right]\)  
    2021 Hard
94. 94. The boxes of masses \(2\, {kg}\) and \(8\, {kg}\) are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass \(8\; {kg}\) to strike the ground starting from rest. (use \(\left.{g}=10\, {m} / {s}^{2}\right)\) (in \({s}\))
    2021 Hard
95. 95. The initial mass of a rocket is \(1000\, {kg} .\) Calculate at what rate the fuel (In \({kg} {s}^{-1}\)) should be burnt so that the rocket is given an acceleration of \(20 \,{ms}^{-2}\). The gases come out at a relative speed of \(500\, {ms}^{-1}\) with respect to the rocket : [Use \( g = 10\, {m} / {s}^{2}\) ] 2021 Medium
96. 96. Two billiard balls of equal mass \(30 \,{g}\) strike a rigid wall with same speed of \(108\, {kmph}\) (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball \('a'\) and ball \('b'\) by the wall along \('X'\) direction is :
    2021 Medium
97. 97. A mass of \(10\; kg\) is suspended by a rope of length \(4 \;\mathrm{m},\) from the ceiling. A force \(\mathrm{F}\) is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of \(45^{\circ}\) with the vertical. Then \(\mathrm{F}\) equals ........... \(N\) (Take \(\mathrm{g}=10 \;\mathrm{ms}^{-2}\) and the rope to be massless) 2020 Medium
98. 98. A particle of mass \(\mathrm{m}\) is fixed to one end of a light spring having force constant \(\mathrm{k}\) and unstretched length \(\ell .\) The other end is fixed. The system is given an angular speed \(\omega\) about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is 2020 Medium
99. 99. A small ball of mass \(m\) is thrown upward with velocity \(u\) from the ground. The ball experiences a resistive force \(mkv ^{2}\) where \(v\) is its speed. The maximum height attained by the ball is  2020 Hard
100. 100. A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate \(\frac{ dM ( t )}{ dt }= bv ^{2}( t ),\) where \(v ( t )\) is its instantaneous velocity. The instantaneous acceleration of the satellite is 2020 Hard

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