Second Law of Motion PYQs: JEE Mains Physics

Showing 1–33 of 33 questions

1. 1. A 4 kg mass moves under the influence of a force \(\vec{F}=\left(4 t^3 \hat{i}-3 t \hat{j}\right) N\) where \(t\) is the time in second. If mass starts from origin at \(t=0\), the velocity and position after \(t=2 s\) will be : 2026 Medium
2. 2. A bead \(P\) sliding on a frictionless semi-circular string \((A C B)\) and it is at point \(S\) at \(t =0\) and at this instant the horizontal component of its velocity is \(v\). Another bead \(Q\) of the same mass as \(P\) is ejected from point \(A\) at \(t =0\) along the horizontal string \(A B\), with the speed \(v\), friction between the beads and the respective strings may be neglected in both cases. Let \(t_p\) and \(t_Q\) be the respective times taken by beads \(P\) and \(Q\) to reach the point \(B\), then the relation between \(t_p\) and \(t_Q\) is
   2026 Hard
3. 3. A block of mass 5 kg is moving on an inclined plane which makes an angle of \(30^{\circ}\) with the horizontal. Friction coefficient between the block and inclined plane surface is \(\frac{\sqrt{3}}{2}\). The force to be applied on the block so that the block will move down without acceleration is ___________ N. 2026 Medium
4. 4. A lift of mass \(1600\) kg is supported by thick iron wire. If the maximum stress which the wire can withstand is \(4 \times 10^8\) N/m\(^2\) and its radius is \(4\) mm, then maximum acceleration the lift can take is _______ m/s\(^2\). (take \(g = 10\) m/s\(^2\) and \(\pi = 3.14\)) 2026 Medium
5. 5. A small block of mass m slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration \(a_{0}.\) The angle between the inclined plane and ground is \(\theta\) and its base length is L. Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane is ___________.
   2026 Easy
6. 6. At \(t=0\), a body of mass \(100\) g starts moving under the influence of a force \((5\hat{i}+10\hat{j})\) N. After \(2\) s its position is \((2x\hat{i}+5y\hat{j})\) m. The ratio \(x:y\) is ______. 2026 Medium
7. 7. The velocity at which \(6\) kg mass (shown in figure) strikes the ground when it is released from a height of \(6\) m above the ground is __________ m/s. Assume pulley is massless and string is light and inextensible. (Take g \(= 10\) m/s\(^2\))
   2026 Medium
8. 8. A block of mass 1 kg , moving along x with speed \(\mathrm{v}_{\mathrm{i}}=10 \mathrm{~m} / \mathrm{s}\) enters a rough region ranging from \(\mathrm{x}=0.1 \mathrm{~m}\) to \(\mathrm{x}=1.9 \mathrm{~m}\). The retarding force acting on the block in this range is \(\mathrm{F}_{\mathrm{r}}=-\mathrm{kx} \mathrm{N}\), with \(\mathrm{k}=10 \mathrm{~N} / \mathrm{m}\). Then the final speed of the block as it crosses rough region is 2025 Medium
9. 9. A body of mass 2 kg moving with velocity of \(\overrightarrow{\mathrm{v}}_{\mathrm{in}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}} \mathrm{ms}^{-1}\) enters into a constant force field of 6 N directed along positive z -axis. If the body remains in the field for a period of \(\frac{5}{3}\) seconds, then velocity of the body when it emerges from force field is 2025 Easy
10. 10. An object with mass 500 g moves along x -axis with speed \(v=4 \sqrt{x} \mathrm{~m} / \mathrm{s}\). The force acting on the object is : 2025 Easy
11. 11. A body of mass \(4 \mathrm{~kg}\) experiences two forces \(\overrightarrow{\mathrm{F}}_1=5 \hat{\mathrm{i}}+8 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{F}}_2=3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}\). The acceleration acting on the body is _______. 2024 Hard
12. 12. A bullet is fired into a fixed target looses one third of its velocity after travelling \(4 \mathrm{~cm}\). It penetrates further \(\mathrm{D} \times 10^{-3} \mathrm{~m}\) before coming to rest. The value of \(D\) is: 2024 Hard
13. 13. A cricket player catches a ball of mass \(120 \mathrm{~g}\) moving with \(25 \mathrm{~m} / \mathrm{s}\) speed. If the catching process is completed in \(0.1 \mathrm{~s}\) then the magnitude of force exerted by the ball on the hand of player will be _______ (in SI unit). 2024 Easy
14. 14. A particle moves in \(\mathrm{x}-\mathrm{y}\) plane under the influence of a force \(\vec{F}\) such that its linear momentum is \(\vec{P}(t)=\hat{i} \cos (k t)-\hat{j} \sin (k t)\). If \(k\) is constant, the angle between \(\overrightarrow{\mathrm{F}}\) and \(\overrightarrow{\mathrm{P}}\) will be _______. 2024 Hard
15. 15. A player caught a cricket ball of mass \(150 \mathrm{~g}\) moving at a speed of \(20 \mathrm{~m} / \mathrm{s}\). If the catching process is completed in \(0.1 \mathrm{~s}\), the magnitude of force exerted by the ball on the hand of the player is _______. 2024 Hard
16. 16. A body of mass \(500\,g\) moves along \(x\)-axis such that it's velocity varies with displacement \(x\) according to the relation \(v =10 \sqrt{ x } m / s\) the force acting on the body is \(...........\,N\) 2023 Medium
17. 17. An average force of \(125\,N\) is applied on a machine gun firing bullets each of mass \(10\,g\) at the speed of \(250\,m / s\) to keep it in position. The number of bullets fired per second by the machine gun is: 2023 Medium
18. 18. 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
19. 19. 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
20. 20. 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
21. 21. 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
22. 22. 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
23. 23. 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
24. 24. 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
25. 25. 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
26. 26. 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
27. 27. 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
28. 28. 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
29. 29. 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
30. 30. A ball is thrown upward with an initial velocity \(V_0\) from the surface of the earth. The motion of the ball is affected by a drag force equal to \(m\gamma {v^2}\) (where \(m\) is mass of the ball, \(v\) is its Instantneous velocity and \(\gamma \) is a constant). Time taken by the ball to rise to its zenith is 2019 Hard
31. 31. A particle of mass \(m\) is acted upon by a force \(F\) given by the empirical law \(F = \frac{R}{{{t^2}}}\,v(t)\). If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot  2016 Hard
32. 32. A body of mass \(5\, kg\) under the action of constant force \(\overrightarrow F  = {F_x}\hat i + {F_y}\hat j\) has velocity at \(t\,= 0\, s\) as \(\overrightarrow v  = \left( {6\hat i - 2\hat j\,m/s} \right)\)  and at \(t\, = 10\,s\) as \(\overrightarrow v  = +6\hat j\,m/s\). The force \(\overrightarrow F \) is  2014 Medium
33. 33. Water is flowing at a speed of \(1.5\, ms^{-1}\) through a horizontal tube of cross-sectional area  \(10^{-2}\, m^2\) and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm. the minimum force that you must exert should be ......... \(N\) (density of water \(= 10^3\, kgm^{-3}\)) 2014 Medium

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