STD 11 - Work,energy,power and collision PYQs: JEE Mains Physics

Showing 1–50 of 191 questions

1. 1. A \(1\) kg block subjected to two simultaneous forces \((2\hat{i} + 3\hat{j} + 4\hat{k})\) N and \((3\hat{i} - \hat{j} - 2\hat{k})\) N is moved a distance of \(25\) m along \((3\hat{i} - 4\hat{j})\) direction. The work done in this process is _____ J. 2026 Medium
2. 2. A body of mass \(1\) kg moves along a straight line with a velocity \(v = 2x^2\). The work done by the body during displacement from \(x = 0\) to \(5\) m is __________ J. 2026 Medium
3. 3. A body of mass \(2\) kg begins to move under the influence of time dependent force \(\vec{F} = (2t\hat{i} + 6t^2\hat{j})\) N, where \(\hat{i}\) and \(\hat{j}\) are unit vectors along \(x\) and \(y\)-axis respectively. The power produced by the force at \(t = 2\) s is _____ W. 2026 Medium
4. 4. A body of mass 2 kg is moving along x -direction such that its displacement as function of time is given by \(x ( t )=\alpha t ^2+\beta t +\gamma m\), where \(\alpha=1 m / s ^2\), \(\beta=1 m / s\) and \(\gamma=1 m\). The work done on the body during the time interval \(t =2 s\) to \(t =3 s\), is _________ J. 2026 Easy
5. 5. A mass of \(1\text{ kg}\) is kept on an inclined plane with \(30°\) inclination with respect to horizontal plane and it is at rest initially. Then the whole assembly is moved up with constant velocity of \(4\text{ m/s}\). The work done by the frictional force in time \(2\text{ s}\) is _______ J. (Take \(g = 10\text{ m/s}^2\)) 2026 Medium
6. 6. A small bob A of mass m is attached to a massless rigid rod of length 1m pivoted at point P and kept at an angle of \( 60^{\circ} \) with vertical as shown in figure. At distance of 1m below point P, an identical bob B is kept at rest on a smooth horizontal surface that extends to a circular track of radius R as shown in figure. If bob B just manages to complete the circular path of radius R upto a point Q after being hit elastically by both A, then radius R is ___________m.
   2026 Hard
7. 7. A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height \(h\) as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height \(h = \alpha R\). The value of \(\alpha\) is _______.
   2026 Medium
8. 8. A spherical ball of mass \(2\) kg falls from a height of \(10\) m and is brought to rest after penetrating \(10\) cm into sand. The average force exerted by sand on the ball is _______ N. (Take \(g = 10\) m/s\(^2\)) 2026 Medium
9. 9. Given below are two statements:
   Statement I: An object moves from position \( r_{1} \) to position \( r_{2} \) under a conservative force field \( \vec{F} \). The work done by the force is \( W=-\int_{r_{1}}^{r_{2}}\vec{F}\cdot d\vec{r} \).
   Statement II Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.
   In the light of above statement, choose the correct answer from the options given below: 2026 Medium
10. 10. In a perfectly inelastic collision, two spheres made of the same material with masses 15 kg and 25 kg , moving in opposite directions with speeds of \(10 m / s\) and \(30 m / s\), respectively, strike each other and stick together. The rise in temperature (in \({ }^{\circ} C\) ), if all the heat produced during the collision is retained by these spheres, is :
    (specific heat of sphere material \(31 cal / kg .{ }^{\circ} C\) and \(1 cal =4.2 J)\) 2026 Easy
11. 11. In case of vertical circular motion of a particle by a thread of length \(r\) if the tension in the thread is zero at an angle \(30^{\circ}\) shown in figure, the velocity at the bottom point (A) of the circular path is ( \(g =\) gravitational acceleration)
    2026 Medium
12. 12. Potential energy (V) versus distance (x) is given by the graph, Rank various regions as per the magnitudes of the force (F) acting on a particle from high to low.
    2026 Hard
13. 13. The rain drop of mass \(1\) g, starts with zero velocity from a height of \(1\) km. It hits the ground with a speed of \(5\) m/s. The work done by the unknown resistive force is _______ J. (take \(g = 10\) m/s\(^2\)) 2026 Medium
14. 14. Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B as shown in figure. The energy stored in A is E . The energy stored in B , when spring constants \(k _{ A }, k _{ B }\) of A and \(B\), respectively satisfy the relation \(4 k _{ A }=3 k _{ B }\), is :
    2026 Medium
15. 15. A bead of mass ' \(m\) ' slides without friction on the wall of a vertical circular hoop of radius ' \(R\) ' as shown in figure. The bead moves under the combined action of gravity and a massless spring ( k ) attached to the bottom of the hoop. The equilibrium length of the spring is ' \(R\) '. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ' R ', would be (spring constant is ' k ', g is accleration due to gravity)
    2025 Hard
16. 16. A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is \(200 \mathrm{~N} / \mathrm{m}\). The block is pushed such that the length of the spring becomes 1 m and then released. At distance \(\mathrm{x} \mathrm{m}(\mathrm{x} \lt 2)\) from the wall. the speed of the block will be : 2025 Medium
17. 17. A block of mass 25 kg is pulled along a horizontal surface by a force at an angle \(45^{\circ}\) with the horizontal. The friction coefficient between the block and the surface is 0.25. The displacement of 5 m of the block is: 2025 Medium
18. 18. A bob of mass \(m\) is suspended at a point \(O\) by a light string of length \(l\) and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity \(v_0\) at the point ' A ', the string becomes slack when, the bob reaches at the point ' D '. The ratio of the kinetic energy of the bob at the points \(B\) and \(C\) is ______ -.
    
    
    2025 Medium
19. 19. A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point \(A\) is \(10 \mathrm{~m} / \mathrm{s}\). The ratio of its kinetic energies at point \(B\) and \(C\) is :
    
    (Take acceleration due to gravity as \(10 \mathrm{~m} / \mathrm{s}^2\) ) 2025 Medium
20. 20. A body of mass 4 kg is placed on a plane at a point P having coordinate \((3,4) \mathrm{m}\). Under the action of force \(\overrightarrow{\mathrm{F}}=(2 \hat{i}+3 \hat{j}) \mathrm{N}\), it moves to a new point Q having coordinates \((6,10) \mathrm{m}\) in 4 sec . The average power and instanteous power at the end of 4 sec are in the ratio of : 2025 Easy
21. 21. A body of mass ' \(m\) ' connected to a massless and unstretchable string goes in verticle circle of radius ' \(R\) 'under gravity \(g\). The other end of the string is fixed at the center of circle. If velocity at top of circular path is \(n \sqrt{g R}\), where, \(n \geqslant 1\), then ratio of kinetic energy of the body at bottom to that at top of the circle is 2025 Hard
22. 22. A force \(\overrightarrow{\mathrm{F}}=2 \hat{i}+\mathrm{b} \hat{j}+\hat{k}\) is applied on a particle and it undergoes a displacement \(\hat{i}-2 \hat{j}-\hat{k}\). What will be the value of \(b\), if work done on the particle is zero. 2025 Easy
23. 23. A force \(\mathrm{F}=\alpha+\beta \mathrm{x}^2\) acts on an object in the x -direction. The work done by the force is 5 J when the object is displaced by 1 m . If the constant \(\alpha=1 \mathrm{~N}\) then \(\beta\) will be ________. 2025 Easy
24. 24. A force \(\mathrm{f}=\mathrm{x}^2 \mathrm{y} \hat{\mathrm{i}}+\mathrm{y}^2 \hat{\mathrm{j}}\) acts on a particle in a plane \(\mathrm{x}+\mathrm{y}=10\). The work done by this force during a displacement from \((0,0)\) to \((4 \mathrm{~m}, 2 \mathrm{~m})\) is Joule (round off to the nearest integer) 2025 Easy
25. 25. A particle is released from height \(S\) above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively. 2025 Easy
26. 26. A sand dropper drops sand of mass \(m(t)\) on a conveyer belt at a rate proportional to the square root of speed \((v)\) of the belt, i.e. \(\frac{\mathrm{dm}}{\mathrm{dt}} \propto \sqrt{v}\). If P is the power delivered to run the belt at constant speed then which of the following relationship is true? 2025 Hard
27. 27. An object of mass 1000 g experiences a time dependent force \(\vec{F}=\left(2 t \hat{i}+3 t^2 \hat{j}\right) N\). The power generated by the force at time \(t\) is : 2025 Medium
28. 28. As shown below, bob \(A\) of a pendulum having massless string of length ' \(R\) ' is released from \(60^{\circ}\) to the vertical. It hits another bob \(B\) of half the mass that is at rest on a friction less table in the center. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take g as acceleration due to gravity.)
    2025 Hard
29. 29. Given below are two statements: one is labelled as Assertion \(\mathbf{A}\) and the other is labelled as Reason \(\mathbf{R}\)
    Assertion A: In a central force field, the work done is independent of the path chosen.
    Reason R: Every force encountered in mechanics does not have an associated potential energy.
    In the light of the above statements, choose the most appropriate answer from the options given below 2025 Easy
30. 30. Which one of the following forces cannot be expressed in terms of potential energy? 2025 Easy
31. 31. A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is _______.
    2024 Hard
32. 32. A block of mass \(1 \mathrm{~kg}\) is pushed up a surface inclined to horizontal at an angle of \(60^{\circ}\) by a force of \(10 \mathrm{~N}\) parallel to the inclined surface as shown in figure. When the block is pushed up by \(10 \mathrm{~m}\) along inclined surface, the work done against frictional force is _______. \(\left[\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right]\)
    2024 Hard
33. 33. A block of mass \(100 \mathrm{~kg}\) slides over a distance of \(10 \mathrm{~m}\) on a horizontal surface. If the co-efficient of friction between the surfaces is \(0.4\) , then the work done against friction (in \(\mathrm{J}\) ) is : 2024 Hard
34. 34. A bob of mass ' \(m\) ' is suspended by a light string of length ' \(L\) '. It is imparted a minimum horizontal velocity at the lowest point \(A\) such that it just completes half circle reaching the top most position B. The ratio of kinetic energies \(\frac{(\text { K.E. })_A}{(\text { K.E. })_B}\) is _______.
    2024 Hard
35. 35. A body is moving unidirectionally under the influence of a constant Power source. Its displacement in time \(t\) is proportional to _______. 2024 Hard
36. 36. A body of \(\mathrm{m} \mathrm{kg}\) slides from rest along the curve of vertical circle from point \(A\) to \(B\) in friction less path. The velocity of the body at \(B\) is _______. (given, \(\mathrm{R}=14 \mathrm{~m}, \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^2\) and \(\sqrt{2}=1.4\) )
    2024 Hard
37. 37. A body of mass \(2 \mathrm{~kg}\) begins to move under the action of a time dependent force given by \(\overrightarrow{\mathrm{F}}=\left(6 \mathrm{t} \hat{\mathrm{i}}+6 \mathrm{t}^2 \hat{\mathrm{j}}\right) \mathrm{N}\). The Power developed by the force at the time \(t\) is given by _______. 2024 Hard
38. 38. A body of mass \(50 \mathrm{~kg}\) is lifted to a height of \(20 \mathrm{~m}\) from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases will be _______.
    2024 Hard
39. 39. A body starts falling freely from height \(\mathrm{H}\) hits an inclined plane in its path at height \(\mathrm{h}\). As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of \(\frac{\mathrm{H}}{\mathrm{h}}\) for which the body will take the maximum time to reach the ground is _______. 2024 Hard
40. 40. A bullet of mass \(50 \mathrm{~g}\) is fired with a speed \(100 \mathrm{~m} / \mathrm{s}\) on a plywood and emerges with \(40 \mathrm{~m} / \mathrm{s}\). The percentage loss of kinetic energy is _______. 2024 Hard
41. 41. A force \(\left(3 x^2+2 x-5\right) N\) displaces a body from \(\mathrm{x}=2 \mathrm{~m}\) to \(\mathrm{x}=4 \mathrm{~m}\). Work done by this force is _______ J. 2024 Hard
42. 42. A particle is placed at the point \(\mathrm{A}\) of a frictionless track \(A B C\) as shown in figure. It is gently pushed toward right. The speed of the particle when it reaches the point \(B\) is _______. \(\left(\right.\) Take \(g=10 \mathrm{~m} / \mathrm{s}^2\) ).
    2024 Hard
43. 43. A particle of mass \(m\) moves on a straight line with its velocity increasing with distance according to the equation \(\mathrm{v}=\alpha \sqrt{\mathrm{x}}\), where \(\alpha\) is a constant. The total work done by all the forces applied on the particle during its displacement from \(\mathrm{x}=0\) to \(\mathrm{x}=\mathrm{d}\), will be _______. 2024 Hard
44. 44. A stationary particle breaks into two parts of masses \(m_A\) and \(m_B\) which move with velocities \(v_A\) and \(V_B\) respectively. The ratio of their kinetic energies \(\left(\mathrm{K}_B: \mathrm{K}_{\mathrm{A}}\right)\) is _______. 2024 Hard
45. 45. An elastic spring under tension of \(3 \mathrm{~N}\) has a lengtha. Its length is \(b\) under tension \(2 \mathrm{~N}\). For its length\((3 a-2 b)\), the value of tension will be_______. \(\mathrm{N}\). 2024 Hard
46. 46. Four particles \(A, B, C, D\) of mass \(\frac{\mathrm{m}}{2}, \mathrm{~m}, 2 \mathrm{~m}, 4 \mathrm{~m}\), have same momentum, respectively. The particle with maximum kinetic energy is _______. 2024 Hard
47. 47. If a rubber ball falls from a height \(h\) and rebounds upto the height of \(h / 2\). The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are _______. 2024 Hard
48. 48. The potential energy function (in J) of a particle in a region of space is given as \(U=\left(2 x^2+3 y^3+2 z\right)\). Here \(\mathrm{x}, \mathrm{y}\) and \(\mathrm{z}\) are in meter. The magnitude of \(\mathrm{x}\) - component of force (in \(\mathrm{N}\) ) acting on the particle at point \(\mathrm{P}(1,2,3)\ \mathrm{m}\) is: 2024 Hard
49. 49. Three bodies \(A, B\) and \(C\) have equal kinetic energies and their masses are \(400 \mathrm{~g}, 1.2 \mathrm{~kg}\) and \(1.6 \mathrm{~kg}\) respectively. The ratio of their linear momenta is _______. 2024 Hard
50. 50. When kinetic energy of a body becomes \(36\) times of its original value, the percentage increase in the momentum of the body will be _______. 2024 Hard

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