STD 11 - Motion in plane PYQs: JEE Mains Physics

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1. 1. A block is sliding down on an inclined plane of slope \(\theta\) and at an instant \(t=0\) this block is given an upward momentum so that it starts moving up on the inclined surface with velocity \(u\). The distance \((S)\) travelled by the block before its velocity become zero, is ___________.
   (\(g=\) gravitational acceleration) 2026 Easy
2. 2. A boy thrown a ball into air at \(45^{\circ}\) from the horizontal to land it on a roof of a building of height H . If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of H is _________ m .
   \(\left( g =10 m / s ^2\right)\) 2026 Medium
3. 3. A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is \(6.4\) m. The speed of the bullets from the gun is ______ m/s.
   (take \(g=10\) m/s\(^2\)) 2026 Easy
4. 4. A projectile is thrown upward at an angle \( 60^{\circ} \) with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is \( 45^{\circ} \) with the horizontal. The initial speed of the projectile is __________ in m/s. 2026 Easy
5. 5. A river of width 200 m is flowing from west to east with a speed of \(18 km / h\). A boat, moving with speed of \(36 km / h\) in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey and also the displacement along the river bank are _________ and _________ respectively. 2026 Medium
6. 6. An object is projected with kinetic energy K from a point A at an angle \(60^{\circ}\) with the horizontal. The ratio of the difference in kinetic energies points B and C to that at point A (see figure), in the absence of air friction is :
   2026 Hard
7. 7. If \(x\) and \(y\) coordinates of a projectile as a function of time \((t)\) are given as \(24t\) and \(43.6t-4.9t^2\), respectively, then the angle (in degrees) made by the projectile with horizontal when \(t=2\) s is ______. 2026 Medium
8. 8. The percentage error in the calculated volume of a sphere, if there is \(2\%\) error in its diameter measurement, is __________. 2026 Medium
9. 9. Two identical bodies, projected with the same speed at two different angles cover the same horizontal range \(R\). If the time of flight of these bodies are \(5\) s and \(10\) s, respectively, then the value of \(R\) is ________ m. (Take \(g=10\) m/s\(^2\)) 2026 Medium
10. 10. Two projectiles are projected with the same initial velocities at the \(15^\circ\) and \(30^\circ\) with respect to the horizontal. The ratio of their ranges is \(1:x\). The value of \(x\) is: 2026 Medium
11. 11. A ball having kinetic energy KE, is projected at an angle of \(60^{\circ}\) from the horizontal. What will be the kinetic energy of ball at the highest point of its flight ? 2025 Easy
12. 12. A ball of mass 100 g is projected with velocity \(20 \mathrm{~m} / \mathrm{s}\) at \(60^{\circ}\) with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is 2025 Medium
13. 13. A helicopter flying horizontally with a speed of \(360 \mathrm{~km} / \mathrm{h}\) at an altitude of 2 km , drops an object at an instant. The object hits the ground at a point O , 20 s after it is dropped. Displacement of ' O ' from the position of helicopter where the object was released is :
    (use acceleration due to gravity \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) and neglect air resistance) 2025 Medium
14. 14. A particle is projected at an angle of \(30^{\circ}\) from horizontal at a speed of \(60 \mathrm{~m} / \mathrm{s}\). The height traversed by the particle in the first second is \(\mathrm{h}_0\) and height traversed in the last second, before it reaches the maximum height, is \(h_1\). The ratio \(h_0: h_1\) is _________
    [Take, \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) ] 2025 Hard
15. 15. A particle is projected with velocity \(u\) so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as \(\frac{n u^2}{25 g}\), where value of \(n\) is : (Given ' \(g\) ' is the acceleration due to gravity). 2025 Easy
16. 16. A river is flowing from west to east direction with speed of \(9 \mathrm{~km} \mathrm{~h}^{-1}\). If a boat capable of moving at a maximum speed of \(27 \mathrm{~km} \mathrm{~h}^{-1}\) in still water, crosses the river in half a minute, while moving with maximum speed at an angle of \(150^{\circ}\) to direction of river flow, then the width of the river is : 2025 Easy
17. 17.
    A string of length \(L\) is fixed at one end and carries a mass of \(M\) at the other end. The mass makes \(\left(\frac{3}{\pi}\right)\) rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is \(\ldots\ldots\) ML. 2025 Hard
18. 18. A tube of length 1 m is filled completely with an ideal liquid of mass 2 M , and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is \(\sqrt{\frac{\mathrm{F}}{\alpha \mathrm{M}}}\) in SI unit. The value of \(\alpha\) is __________. 2025 Hard
19. 19. The maximum speed of a boat in still water is \(27 \mathrm{~km} / \mathrm{h}\). Now this boat is moving downstream in a river flowing at \(9 \mathrm{~km} / \mathrm{h}\). A man in the boat throws a ball vertically upwards with speed of \(10 \mathrm{~m} / \mathrm{s}\). Range of the ball as observed by an observer at rest on the river bank, is _______ cm. (Take \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\)) 2025 Medium
20. 20. The position vector of a moving body at any instant of time is given as \(\vec{r}=\left(5 t^2 \hat{i}-5 t \hat{j}\right) \mathrm{m}\). The magnitude and direction of velocity at \(t=2 \mathrm{~s}\) is, 2025 Medium
21. 21. Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball. \(T_1\) and \(T_2\) are the total flying times of first and second ball, respectively, then the ratio of \(T_1\) and \(T_2\) is : 2025 Easy
22. 22. Two cars \(P\) and \(Q\) are moving on a road in the same direction. Acceleration of car \(P\) increases linearly with time whereas car \(Q\) moves with a constant acceleration. Both cars cross each other at time \(t=0\), for the first time. The maximum possible number of crossing(s) (including the crossing at \(t=0)\) is ________. 2025 Medium
23. 23. Two projectiles are fired from ground with same initial speeds from same point at angles \(\left(45^{\circ}+\alpha\right)\) and \(\left(45^{\circ}-\alpha\right)\) with horizontal direction. The ratio of their times of flights is 2025 Easy
24. 24. Two projectiles are fired with same initial speed from same point on ground at angles of \(\left(45^{\circ}-\alpha\right)\) and \(\left(45^{\circ}+\alpha\right)\), respectively, with the horizontal direction. The ratio of their maximum heights attained is : 2025 Medium
25. 25. A ball of mass \(0.5 \mathrm{~kg}\) is attached to a string of length \(50 \mathrm{~cm}\). The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is \(400 \mathrm{~N}\). The maximum possible value of angular velocity of the ball in rad/s is _______. 2024 Hard
26. 26. A ball rolls off the top of a stairway with horizontal velocity \(\mathrm{u}\). The steps are \(0.1 \mathrm{~m}\) high and \(0.1 \mathrm{~m}\) wide. The minimum velocity \(\mathrm{u}\) with which that ball just hits the step \(5\) of the stairway will be \(\sqrt{\mathrm{x}} \mathrm{ms}^{-1}\) where \(\mathrm{x}=\) _______ [use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) ]. 2024 Hard
27. 27. A body of mass \(M\) thrown horizontally with velocity \(v\) from the top of the tower of height \(\mathrm{H}\) touches the ground at a distance of \(100 \mathrm{~m}\) from the foot of the tower. A body of mass \(2 \mathrm{M}\) thrown at a velocity \(\frac{v}{2}\) from the top of the tower of height \(4 \mathrm{H}\) will touch the ground at a distance of _______. 2024 Hard
28. 28. A circular table is rotating with an angular velocity of \(\omega\) \(\mathrm{rad} / \mathrm{s}\) about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of \(1 \mathrm{~m}\) on the groove. All the surface are smooth. If the radius of the table is \(3 \mathrm{~m}\), the radial velocity of the ball w.r.t. the table at the time ball leaves the table is \(x \sqrt{2} \omega\) \(\mathrm{m} / \mathrm{s}\), where the value of \(x\) is _______.
    2024 Hard
29. 29. A clock has \(75 \mathrm{~cm}, 60 \mathrm{~cm}\) long second hand and minute hand respectively. In \(30\) minutes duration the tip of second hand will travel \(x\) distance more than the tip of minute hand. The value of \(x\) in meter is nearly _______. (Take \(\pi=3.14\) ) 2024 Hard
30. 30. A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius \(9 \mathrm{~m}\) and completes \(120\) revolutions in \(3\) minutes. The magnitude of centripetal acceleration of monkey is _______ (in \(\mathrm{m} / \mathrm{s}^2\) ). 2024 Hard
31. 31. A particle is moving in a circle of radius \(50 \mathrm{~cm}\) in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at \(t=0\) is \(4 \mathrm{~m} / \mathrm{s}\), the time taken to complete the first revolution will be \(\frac{1}{\alpha}\left[1-\mathrm{e}^{-2 \pi}\right] \mathrm{s}\), where \(\alpha=\) _______. 2024 Hard
32. 32. A particle moving in a circle of radius \(R\) with uniform speed takes time \(\mathrm{T}\) to complete one revolution. If this particle is projected with the same speed at an angle \(\theta\) to the horizontal, the maximum height attained by it is equal to \(4 R\). The angle of projection \(\theta\) is then given by _______. 2024 Hard
33. 33. A stone of mass \(900 \mathrm{~g}\) is tied to a string and moved in a vertical circle of radius \(1 \mathrm{~m}\) making \(10\  \mathrm{rpm}\). The tension in the string, when the stone is at the lowest point is _______. (if \(\pi^2=9.8\) and \(g=9.8 \mathrm{~m} / \mathrm{s}^2\) ) 2024 Hard
34. 34. Projectiles \(A\) and \(B\) are thrown at angles of \(45^{\circ}\) and \(60^{\circ}\) with vertical respectively from top of a \(400 \mathrm{~m}\) high tower. If their ranges and times of flight are same, the ratio of their speeds of projection \(v_A: v_B\) is _______. 2024 Hard
35. 35. The angle of projection for a projectile to have same horizontal range and maximum height is _______. 2024 Hard
36. 36. The co-ordinates of a particle moving in \(x-y\) plane are given by :  \(\mathrm{x}=2+4 \mathrm{t}, \mathrm{y}=3 \mathrm{t}+8 \mathrm{t}^2 .\) The motion of the particle is _______. 2024 Hard
37. 37. The maximum height reached by a projectile is \(64 \mathrm{~m}\). If the initial velocity is halved, the new maximum height of the projectile is _______ \(\mathrm{m}\). 2024 Hard
38. 38. A car is moving on a circular path of radius \(600\,m\) such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of \(54\,km / hr\) is \(t \left(1- e ^{-\pi / 2}\right)\,s\). The value of \(t\) is \(.............\). 2023 Hard
39. 39. A child stands on the edge of the cliff \(10\,m\) above the ground and throws a stone horizontally with an initial speed of \(5\,ms ^{-1}\). Neglecting the air resistance, the speed with which the stone hits the ground will be \(..........ms ^{-1}\) (given, \(g =10\,ms ^{-2}\)) 2023 Medium
40. 40. A particle is moving with constant speed in a circular path. When the particle turns by an angle \(90^{\circ}\), the ratio of instantaneous velocity to its average velocity is \(\pi: x \sqrt{2}\). The value of \(x\) will be \(.........\) 2023 Hard
41. 41. A particle of mass \(100\,g\) is projected at time \(t =0\) with a speed \(20\,ms ^{-1}\) at an angle \(45^{\circ}\) to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time \(t=2\,s\) is found to be \(\sqrt{ K }\,kg\,m ^2 / s\). The value of \(K\) is \(............\) \(\left(\right.\) Take \(\left.g =10\,ms ^{-2}\right)\)
    2023 Hard
42. 42. A projectile fired at \(30^{\circ}\) to the ground is observed to be at same height at time \(3 s\) and \(5 s\) after projection, during its flight. The speed of projection of the projectile is \(.........\,ms ^{-1}\)(Given \(g=10\,m s ^{-2}\) ) 2023 Hard
43. 43. A projectile is projected at \(30^{\circ}\) from horizontal with initial velocity \(40\,ms ^{-1}\). The velocity of the projectile at \(t =2\,s\) from the start will be \(........\) (Given \(g =10\,m / s ^2\) ) 2023 Hard
44. 44. A stone is projected at angle \(30^{\circ}\) to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be : 2023 Medium
45. 45. A stone tied to \(180 cm\) long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is \(\frac{1936}{ x }\,ms ^{-2}\). The value of \(x.........\left(\text { Take } \pi=\frac{22}{7}\right)\) 2023 Easy
46. 46. An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at \(x =+2\,m\), its velocity is \(-4 \hat{ j }\, m / s\). The object's velocity \((v)\) and acceleration \((a)\) at \(x =-2\,m\) will be 2023 Medium
47. 47. As shown in the figure, a particle is moving with constant speed \(\pi\,m / s\). Considering its motion from \(A\) to \(B\), the magnitude of the average velocity is:
    2023 Hard
48. 48. For particle \(P\) revolving round the centre \(O\) with radius of circular path \(r\) and angular velocity \(\omega\), as shown in below figure, the projection of \(OP\) on the \(x\)-axis at time \(t\) is \(.................\).
    2023 Easy
49. 49. Given below are two statements : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : When a body is projected at an angle \(45^{\circ}\), it's range is maximum. Reason \(R\) : For maximum range, the value of \(\sin 2 \theta\) should be equal to one. In the light of the above statements, choose the correct answer from the options given below : 2023 Medium
50. 50. The initial speed of a projectile fired from ground is \(u\). At the highest point during its motion, the speed of projectile is \(\frac{\sqrt{3}}{2} u\). The time of flight of the projectile is: 2023 Medium

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