STD 11 - Motion in plane PYQs: JEE Mains Physics – Page 2

Showing 51–100 of 114 questions

51. 51. The maximum vertical height to which a man can throw a ball is \(136\,m\). The maximum horizontal distance upto which he can throw the same ball is \(.....\,m\) 2023 Medium
52. 52. The range of the projectile projected at an angle of \(15^{\circ}\) with horizontal is \(50\,m\). If the projectile is projected with same velocity at an angle of \(45^{\circ}\) with horizontal, then its range will be \(........\,m\) 2023 Medium
53. 53. The speed of a swimmer is \(4\,km\,h ^{-1}\) in still water. If the swimmer makes his strokes normal to the flow of river of width \(1\,km\), he reaches a point \(750 \,m\) down the stream on the opposite bank.The speed of the river water is \(.........km h ^{-1}\) 2023 Medium
54. 54. The trajectory of projectile, projected from the ground is given by \(y=x-\frac{x^2}{20}\). Where \(x\) and \(y\) are measured in meter. The maximum height attained by the projectile will be \(...........\,m\) 2023 Medium
55. 55. Two objects are projected with same velocity ' \(u\) ' however at different angles \(\alpha\) and \(\beta\) with the horizontal. If \(\alpha+\beta=90^{\circ}\), the ratio of horizontal range of the first object to the \(2^{\text {nd }}\) object will be : 2023 Medium
56. 56. Two projectiles \(A\) and \(B\) are thrown with initial velocities of \(40\,m / s\) and \(60\,m / s\) at angles \(30^{\circ}\) and \(60^{\circ}\) with the horizontal respectively. The ratio of their ranges respectively is \(\left( g =10\,m / s ^2\right)\) 2023 Easy
57. 57. Two projectiles are projected at \(30^{\circ}\) and \(60^{\circ}\) with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is: 2023 Easy
58. 58. A ball is projected from the ground with a speed \(15 \,ms ^{-1}\) at an angle \(\theta\) with horizontal so that its range and maximum height are equal, then \(tan\,\theta\) will be equal to  2022 Medium
59. 59. A ball is projected with kinetic energy \(E\), at an angle of \(60^{\circ}\) to the horizontal. The kinetic energy of this ball at the highest point of its flight will become. 2022 Medium
60. 60. A ball of mass \(m\) is thrown vertically upward. Another ball of mass \(2\,m\) is thrown an angle \(\theta\) with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is \(\frac{1}{x}\). The value of \(x\) is \(.....\) 2022 Medium
61. 61. A body is projected from the ground at an angle of \(45^{\circ}\) with the horizontal. Its velocity after \(2s\) is \(20 \,ms ^{-1}\). The maximum height reached by the body during its motion is \(m\). (use \(g =10\, ms ^{-2}\) ) 2022 Hard
62. 62. A boy ties a stone of mass \(100 \,g\) to the end of a \(2\) \(m\) long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of \(80 \,N\). If the maximum speed with which the stone can revolve is \(\frac{ K }{\pi} rev\). / \(min\). The value of \(K\) is (Assume the string is massless and unstretchable) 2022 Medium
63. 63. A fighter jet is flying horizontally at a certain altitude with a speed of \(200 \; ms ^{-1}\). When it passes directly overhead an anti-aircraft gun, bullet is fired from the gun, at an angle \(\theta\) with the horizontal, to hit the jet. If the bullet speed is \(400 \; m / s\), the value of \(\theta\) will be \(\dots \; {}^o\) 2022 Medium
64. 64. A fly wheel is accelerated uniformly from rest and rotates through \(5 \,rad\) in the first second. The angle rotated by the fly wheel in the next second, will be.........\(rad\) 2022 Easy
65. 65. A girl standing on road holds her umbrella at \(45^{\circ}\) with the vertical to keep the rain away. If she starts running without umbrella with a speed of \(15 \sqrt{2} \; kmh ^{-1}\), the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is ...........  \(kmh ^{-1}\) 2022 Medium
66. 66. A \(NCC\) parade is going at a uniform speed of \(9\,km / h\) under a mango tree on which a monkey is sitting at a height of \(19.6\,m\). At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is \(...m\) (Given \(g=9.8\,m / s ^{2}\) ) 2022 Medium
67. 67. A projectile is launched at an angle ' \(\alpha\) ' with the horizontal with a velocity \(20 \; ms ^{-1}\). After \(10 s\), its inclination with horizontal is ' \(\beta\) '. The value of \(\tan \beta\) will be : \(\left( g =10 \; ms ^{-2}\right)\) 2022 Hard
68. 68. A projectile is projected with velocity of \(25\, m / s\) at an angle \(\theta\) with the horizontal. After t seconds its inclination with horizontal becomes zero. If \(R\) represents horizontal range of the projectile, the value of \(\theta\) will be : [use \(g =10 m / s ^{2}\) ] 2022 Medium
69. 69. An object is projected in the air with initial velocity \(u\) at an angle \(\theta\). The projectile motion is such that the horizontal range \(R\), is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be \(.......\) degree. 2022 Medium
70. 70. At time \(t =0\) a particle starts travelling from a height \(7\,\hat{z} cm\) in a plane keeping \(z\) coordinate constant. At any instant of time it's position along the \(x\) and \(y\) directions are defined as \(3\,t\) and \(5\,t^{3}\) respectively. At \(t =1\,s\) acceleration of the particle will be. 2022 Medium
71. 71. Given below are two statements. One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion A :Two identical balls \(A\) and \(B\) thrown with same velocity '\(u\) ' at two different angles with horizontal attained the same range \(R\). If \(A\) and \(B\) reached the maximum height \(h_{1}\) and \(h_{2}\) respectively, then \(R =4 \sqrt{ h _{1} h _{2}}\) Reason R: Product of said heights. \(h _{1} h _{2}=\left(\frac{u^{2} \sin ^{2} \theta}{2 g }\right) \cdot\left(\frac{u^{2} \cos ^{2} \theta}{2 g }\right)\) Choose the \(CORRECT\) answer  2022 Medium
72. 72. If the initial velocity in horizontal direction of a projectile is unit vector \(\hat{i}\) and the equation of trajectory is \(y =5 x (1- x )\). The \(y\) component vector of the initial velocity is. (Take \(g=10\,m / s ^{2}\) ) 2022 Medium
73. 73. Motion of a particle in \(x - y\) plane is described by a set of following equations \(x=4 \sin \left(\frac{\pi}{2}-\omega t\right) m\) and \(y=4 \sin (\omega t) m\). The path of particle will be  2022 Medium
74. 74. Two projectile thrown at \(30^{\circ}\) and \(45^{\circ}\) with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is 2022 Medium
75. 75. Two projectiles are thrown with same initial velocity making an angle of \(45^{\circ}\) and \(30^{\circ}\) with the horizontal respectively. The ratio of their respective ranges will be. 2022 Easy
76. 76. A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a : 2021 Medium
77. 77. A butterfly is flying with a velocity \(4 \sqrt{2} \,{m} / {s}\) in North-East direction. Wind is slowly blowing at \(1\) \({m} / {s}\) from North to South. The resultant displacement of the butterfly in \(3\, seconds\) is \(....\,{m}.\) 2021 Hard
78. 78. A helicopter is flying horizontally with a speed \('v'\) at an altitude \('{h}'\) has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped? 2021 Hard
79. 79. A huge circular arc of length \(4.4\) \(ly\) subtends an angle \('4 {s}'\) at the centre of the circle. How long it would take for a body to complete \(4\) revolution if its speed is \(8 \;AU\;per\, second \;?\) Given : \(1\, {ly}=9.46 \times 10^{15} \,{m},\) \(\, {AU}=1.5 \times 10^{11}\, {m}\) 2021 Hard
80. 80. A mosquito is moving with a velocity \(\overrightarrow{ v }=0.5 t ^{2} \hat{ i }+3 t \hat{ j }+9 \hat{ k }\, m / s\) and accelerating in uniform conditions. What will be the direction of mosquito after \(2 \,s\) ? 2021 Hard
81. 81. A particle is moving with uniform speed along the circumference of a circle of radius \(R\) under the action of a central fictitious force \(F\) which is inversely proportional to \(R ^{3}\). Its time period of revolution will be given by 2021 Hard
82. 82. A particle of mass \({m}\) is suspended from a ceiling through a string of length \(L\). The particle moves in a horizontal circle of radius \(r\) such that \({r}=\frac{{L}}{\sqrt{2}}\). The speed of particle will be: 2021 Hard
83. 83. A person is swimming with a speed of \(10\, m /s\) s at an angle of \(120^{\circ}\) with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is \('x'\) \(m / s\). The value of \('x'\) to the nearest integer is .............. 2021 Medium
84. 84. A player kicks a football with an initial speed of \(25\, {ms}^{-1}\) at an angle of \(45^{\circ}\) from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take g \(=10 \,{ms}^{-2}\) ) 2021 Medium
85. 85. A swimmer can swim with velocity of \(12 \,km / h\) in still water. Water flowing in a river has velocity \(6\, km / h\). The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ........\(^{\circ}\). (Round off to the Nearest Integer) (find the angle in degree) 2021 Hard
86. 86. A swimmer wants to cross a river from point \(A\) to point \(B\). Line \(A B\) makes an angle of \(30^{\circ}\) with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle \(\theta\) with the line \({AB}\) should be \(^{\circ}\), so that the swimmer reaches point \({B}\).
    2021 Medium
87. 87. The projectile motion of a particle of mass \(5\, g\) is shown in the figure. The initial velocity of the particle is \(5 \sqrt{2}\, ms ^{-1}\) and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points \(A\) and \(B\) is \(x \times 10^{-2}\, kgms ^{-1} .\) The value of \(x ,\) to the nearest integer, is ...... .
    2021 Hard
88. 88. The ranges and heights for two projectiles projected with the same initial velocity at angles \(42^{\circ}\) and \(48^{\circ}\) with the horizontal are \({R}_{1}, {R}_{2}\) and \({H}_{1}\), \({H}_{2}\) respectively. Choose the correct option: 2021 Medium
89. 89. The trajectory of a projectile in a vertical plane is \(y =\alpha x -\beta x ^{2},\) where \(\alpha\) and \(\beta\) are constants and \(x \& y\) are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection \(\theta\) and the maximum height attained \(H\) are respectively given by :- 2021 Hard
90. 90. 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 \(60^{\circ}\) with respect to the vertical if the girl moves further by a distance \(2.464\, d\) (point \(C\) ). Then the height \(h _{2}\) is (given tan \(\left.30^{\circ}=0.5774\right)\)\(.......\)
    2020 Hard
91. 91. A particle is moving along the \(x-\)axis with its coordinate with the time '\(t\)' given be \(\mathrm{x}(\mathrm{t})=10+8 \mathrm{t}-3 \mathrm{t}^{2} .\) Another particle is moving the \(y-\)axis with its coordinate as a function of time given by \(\mathrm{y}(\mathrm{t})=5-8 \mathrm{t}^{3} .\) At \(\mathrm{t}=1\; \mathrm{s},\) the speed of the second particle as measured in the frame of the first particle is given as \(\sqrt{\mathrm{v}} .\) Then \(\mathrm{v}\) (in \(\mathrm{m} / \mathrm{s})\) is 2020 Medium
92. 92. A particle moves such that its position vector \(\overrightarrow{\mathrm{r}}(\mathrm{t})=\cos \omega \mathrm{t} \hat{\mathrm{i}}+\sin \omega \mathrm{t} \hat{\mathrm{j}}\) where \(\omega\) is a constant and \(t\) is time. Then which of the following statements is true for the velocity \(\overrightarrow{\mathrm{v}}(\mathrm{t})\) and acceleration \(\overrightarrow{\mathrm{a}}(\mathrm{t})\) of the particle 2020 Medium
93. 93. A particle starts from the origin at \(\mathrm{t}=0\) with an initial velocity of \(3.0 \hat{\mathrm{i}} \;\mathrm{m} / \mathrm{s}\) and moves in the \(x-y\) plane with a constant acceleration \((6.0 \hat{\mathrm{i}}+4.0 \hat{\mathrm{j}}) \;\mathrm{m} / \mathrm{s}^{2} .\) The \(\mathrm{x}\) -coordinate of the particle at the instant when its \(y-\)coordinate is \(32\;\mathrm{m}\) is \(D\) meters. The value of \(D\) is 2020 Medium
94. 94. Starting from the origin at time \(t=0,\) with initial velocity \(5 \hat{ j }\, ms ^{-1},\) a particle moves in the \(x-y\) plane with a constant acceleration of \((10 \hat{ i }+4 \hat{ j })\, ms ^{-2}\). At time \(t\), its coordinates are \(\left(20\, m , y _{0}\, m \right) .\) The values of \(t\) and \(y _{0},\) are respectively 2020 Medium
95. 95. 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 \((1+\beta) v ,\) this angle changes to \(45^{\circ} .\) The value of \(\beta\) is close to\(......\) 2020 Hard
96. 96. A body is projected at \(t = 0\) with a velocity \(10\,ms^{-1}\) at an angle of \(60^o\) with the horizontal. The radius of curvature of its trajectory at \(t=1\,s\) is \(R.\) Neglecting air resistance and taking acceleration due to gravity \(g = 10\,ms^{-2},\) the radius of \(R\) is   ........ \(m\) 2019 Hard
97. 97. A particle moves from the point \(\left( {2.0\hat i + 4.0\hat j} \right)\,m\), at \(t = 0\) with an initial velocity \(\left( {5.0\hat i + 4.0\hat j} \right)\,m{s^{ - 1  }}\). It is acted upon by a constant force which produces a constant acceleration \(\left( {4.0\hat i + 4.0\hat j} \right)\,m{s^{ - 2}}\). What is the distance of the particle from the origin at time \(2\,s\) 2019 Medium
98. 98. A plane is inclined at an angle \(\alpha  = 30^o\) with respect to the horizontal. A particle is projected with a speed \(u = 2\,ms^{-1},\) from the base of the plant, making an angle \(\theta = 15^o\) with respect to the plane as shown in the figure. The distance from the base at which the particle hits the plane is close to  ........ \(cm\) (Take \(g = 10\,ms^2\) )
    2019 Hard
99. 99. A shell is fired from a fixed artillery gun with an initial speed \(u\) such that it hits the target on the ground at a distance \(R\) from it. If \(t_1\) and \(t_2\) are the values of the time taken by it to hit the target in two possible ways, the product \(t_1t_2\) is 2019 Hard
100. 100. A smooth wire of length \(2\pi r\) 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 \(\omega\) 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 \(\omega^2\) is equal to
     2019 Hard

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