STD 11 - System of particles and rotational motion PYQs: JEE Mains Physics

Showing 1–50 of 369 questions

1. 1. A circular disc has radius \(R_1\) and thickness \(T_1\). Another circular disc made of the same material has radius \(R_2\) and thickness \(T_2\). If the moment of inertia of both discs are same and \(\frac{R_1}{R_2}=2\) then \(\frac{T_1}{T_2}=\frac{1}{\alpha}\).The value of \(\alpha\) is __________ . 2026 Hard
2. 2. A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to a 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m is ___________ J. (\(g=10~m/s^{2}\)) 2026 Medium
3. 3. A LCR series circuit driven with \(E_{rms} = 90\) V at frequency \(f_d = 30\) Hz has resistance \(R = 80\,\Omega\), an inductance with inductive reactance \(X_L = 20.0\,\Omega\) and capacitance with capacitive reactance \(X_C = 80.0\,\Omega\). The power factor of the circuit is _______. 2026 Medium
4. 4. A particle is rotating in a circular path and at any instant its motion can be described as \(\theta = \dfrac{5t^4}{40} - \dfrac{t^3}{3}\). The angular acceleration of the particle after \(10\) seconds is _______ rad/s\(^2\). 2026 Medium
5. 5. A solid cylinder having radius \(R\) and length \(L\) is slipping on a rough horizontal plane. At time \(t=0\) the cylinder has a translational velocity \(v_0=49\) m/s, perpendicular to its axis and a rotational velocity \(v_0/4R\) about the centre. The time taken by the cylinder to start rolling is ________ seconds. (coefficient of kinetic friction \(\mu_K=0.25\) and \(g=9.8\) m/s\(^2\)) 2026 Hard
6. 6. A solid sphere (\(A\)) of mass \(5m\) and a spherical shell (\(B\)) of mass \(m\), both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of \(A\) and \(B\), they start rolling without slipping with an acceleration of \(a_A\) and \(a_B\), respectively. The ratio of \(a_A\) and \(a_B\) is __________. 2026 Hard
7. 7. A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is __________ \( kg.m^{2} \). 2026 Easy
8. 8. A solid sphere of mass \(M\) and radius \(R\) is divided into two unequal parts. The smaller part having mass \(M/8\) is converted into a sphere of radius \(r\) and the larger part is converted into a circular disc of thickness \(t\) and radius \(2R\). If \(I_1\) is moment of inertia of a sphere having radius \(r\) about an axis through its centre and \(I_2\) is the moment of inertia of a disc about its diameter, the ratio of their moment of inertia \(I_2/I_1 = \) _____. 2026 Hard
9. 9. A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from its centre. The radius of gyration about this axis is \(\sqrt{n}\) cm. The value of n is 2026 Easy
10. 10. A solid sphere of radius \(4\) cm and mass \(5\) kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of \(1200\) rpm. It is brought to rest in \(10\) s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are _______ and _______ respectively. 2026 Medium
11. 11. A thin uniform rod \(( X )\) of mass M and length L is pivoted at a height \(\left(\frac{ L }{3}\right)\) as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top, is _________ . (g = gravitational acceleration)
    2026 Hard
12. 12. A uniform bar of length 12 cm and mass 20 m lies on a smooth horizontal table. Two point masses m and 2 m are moving in opposite directions with same speed of v and in the same plane as the bar. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency \( \omega \). The ratio of v and \( \omega \) is:
    2026 Medium
13. 13. A uniform rod of mass m and length \(l\) suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is _________.(g acceleration due to gravity)
    2026 Easy
14. 14. A uniform solid cylinder of length \(L\) and radius \(R\) has moment of inertia about its axis equal to \(I_1\). A small co-centric cylinder of length \(L / 2\) and radius \(R / 3\) carved from this cylinder has moment of inertia about its axis equals to \(I_2\). The ratio \(I_1 / I_2\) is _________ . 2026 Hard
15. 15. A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first \(2\text{ s}\) it rotates through an angle \(\theta_1\) and in the next \(2\text{ s}\) it rotates through an angle \(\theta_2\). The ratio \(\dfrac{\theta_2}{\theta_1}\) is _______. 2026 Medium
16. 16. Given below are two statements:
    Statement I: For a mechanical system of many particles total kinetic energy is the sum of kinetic energies of all the particles.
    Statement II: The total kinetic energy can be the sum of kinetic energy of the center of mass w.r.t. to the origin and the kinetic energy of all the particles w.r.t. the center of mass as the reference.
    In the light of the above statements,choose the correct answer from the options given below: 2026 Hard
17. 17. Moment of inertia about an axis \(AB\) for a rod of mass \(40\) kg and length \(3\) m is same as that of a solid sphere of mass of \(10\) kg and radius \(R\) about an axis parallel to \(AB\) axis with separation of \(3\) m as shown in figure below. The value of \(R\) is given as \(\sqrt{\dfrac{\alpha}{2}}\). The value of \(\alpha\) is _______.
    2026 Medium
18. 18. Suppose there is a uniform circular disc of mass M kg and radius r m shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about the axis A of the disc is given by \(\frac{ x }{256} Mr ^2\). The value of x is ___________.
    2026 Easy
19. 19. The moment of inertia of a square loop made of four uniform solid cylinders, each having radius R and length \(L ( R < L )\) about an axis passing through the mid points of opposite sides, is (Take the mass of the entire loop as M ) : 2026 Hard
20. 20. The position of center of mass of three masses \(2\) kg, \(3\) kg and \(15\) kg placed with respect to mid point (\(p\)) of normal bisector, as shown in the figure is _______.
    2026 Hard
21. 21. The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of the rim. The rim and each rod have a mass of M . Two blocks of mass of M and m are attached to two ends of a light string passing over the pulley, which is hinged to rotate freely in vertical plane about its centre. The magnitudes of the acceleration experienced by the blocks is _________ (assume no slipping of string on pulley.)
    2026 Easy
22. 22. Two blocks of masses \(2\) kg and \(1\) kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held at rest at the same horizontal level and then released. The distance traversed by the centre of mass in \(2\) s is _______ m. (Take \(g = 10\) m/s\(^2\))
    2026 Hard
23. 23. Two cars A and B each of mass \(10^3 kg\) are moving on parallel tracks separated by a distance of 10 m , in same direction with speeds \(72 km / h\) and \(36 km / h\). The magnitude of angular momentum of car \(A\) with respect to car \(B\) is _________ J.s. 2026 Hard
24. 24. Two circular discs of radius each 10 cm are joined at their centres by a rod of length 30 cm and mass 600 gm as shown in figure.
    If the mass of each disc is 600 gm and applied torque between two discs is \(43 \times 10^{5}\) dyne cm, the angular acceleration of the discs about the given axis \(AB\) is ___________\(rad/s^{2}\).
    2026 Hard
25. 25. Two identical bodies \(A\) and \(B\) of equal masses have initial velocities \(\vec{v_1} = 4\hat{i}\) m/s and \(\vec{v_2} = 4\hat{j}\) m/s respectively. The body \(A\) has acceleration \(\vec{a_1} = 6\hat{i} + 6\hat{j}\) m/s\(^2\) while the acceleration of the other body \(B\) is zero. The centre of mass of the two bodies moves in __________ path. 2026 Hard
26. 26. Two identical thin rods of mass M kg and length L m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpendicular to the plane of the rods is \(\frac{x}{2} M L^2 kg m ^2\). The value of \(x\) is _________.
    2026 Easy
27. 27. Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm . When released from rest the heavier mass is observed to fall 81 cm in 9 s . The rotational inertia of the pulley is _________ \(kg \cdot m ^2\).\(\left( g =9.8 m / s ^2\right)\) 2026 Hard
28. 28. Two masses m and 2m are connected by a light string going over a pulley (disc) of mass 30m with radius r = 0.1 m. The pulley is mounted in a vertical plane and it is free to rotate about its axis. The 2m mass is released from rest and its speed when it has descended through a height of 3.6 m is __________ m/s. (Assume string does not slip and \( g=10 m/s^{2} \)) 2026 Medium
29. 29. Two small balls with masses m and 2 m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is \(L\) about an axis (A) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about A is : 2026 Hard
30. 30. When the position vector \(\overrightarrow{ r }=x \hat{ i }+y \hat{ j }+z \hat{ k }\) changes sign as \(-\overrightarrow{ r }\), which one of the following vector will not flip under sign change ? 2026 Easy
31. 31. \(\mathrm{A}, \mathrm{B}\) and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed as shown in figure.
    
    The moment of inertia of the given system about \(P Q\) is \(\frac{X}{15} I\), where \(I\) is the moment of inertia of the disc about its diameter. The value of x is _______. 2025 Medium
32. 32. A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that \(\theta(t)=5 t^2-8 t\), where \(\theta(t)\) is the angular position of the rotating disc as a function of time \(t\). How much power is delivered by the applied torque, when \(t=2 s\) ? 2025 Medium
33. 33. A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the plane is \(\sqrt{\frac{x}{5}}\) where \(\mathrm{x}=\) _____ 2025 Medium
34. 34. A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest. If a steady pull of 20 N is applied on the cord, the angular velocity of the wheel, after the cord is unwound by 1 m , would be :
    2025 Easy
35. 35. A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg , kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is
    2025 Easy
36. 36. A rod of length 5 L is bent right angle keeping one side length as 2 L.
    
    The position of the centre of mass of the system: (Consider \(\mathrm{L}=10 \mathrm{~cm}\)) 2025 Medium
37. 37. A rod of linear mass density ' \(\lambda\) ' and length ' \(L\) ' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameter is : 2025 Hard
38. 38. A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be \(t_1\) and \(t_2\), respectively, then... 2025 Easy
39. 39. A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and Rotational Equilibrium is : 2025 Hard
40. 40. A solid sphere of mass ' \(m\) ' and radius ' \(r\) ' is allowed to roll without slipping from the highest point of an inclined plane of length ' \(L\) ' and makes an angle \(30^{\circ}\) with the horizontal. The speed of the particle at the bottom of the plane is \(v_1\). If the angle of inclination is increased to \(45^{\circ}\) while keeping \(L\) constant. Then the new speed of the sphere at the bottom of the plane is \(v_2\). The ratio \(v_1^2: v_2^2\) is: 2025 Hard
41. 41. A solid sphere with uniform density and radius R is rotating initially with constant angular velocity \(\left(\omega_1\right)\) about its diameter. After some time during the rotation its starts loosing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius become \(R / 2\) is \(x \omega_1\). The value of \(x\) is ________ 2025 Medium
42. 42. A square Lamina OABC of length 10 cm is pivoted at 'O'. Forces act at Lamina as shown in figure. If Lamina remains stationary, then the magnitude of F is :
    2025 Medium
43. 43. A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of \(25 \pi \mathrm{Nm}\) for 40 s, the speed increases to 2100 rpm. The diameter of the disk is ________ m. 2025 Medium
44. 44. A uniform circular disc of radius ' R ' and mass ' M ' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius \(\mathrm{R} / 2\) is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.
    2025 Medium
45. 45. A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is 2025 Easy
46. 46. A uniform solid cylinder of mass ' \(m\) ' and radius ' \(r\) ' rolls along an inclined rough plane of inclination \(45^{\circ}\). If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be 2025 Medium
47. 47. A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is \(8 \mathrm{~m} / \mathrm{s}\). The speed of the particle on the rim of the wheel at the same level as the centre of wheel, will be : 2025 Medium
48. 48.
    A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in figure. The established torque produces an angular acceleration of \(2 \mathrm{~rad} / \mathrm{s}^2\). Moment of inertia of the wheel is _____ \(\mathrm{kg} \mathrm{m}^2\).
    (Acceleration due to gravity \(=10 \mathrm{~m} / \mathrm{s}^2\)) 2025 Medium
49. 49. An object of mass ' m ' is projected from origin in a vertical \(x y\) plane at an angle \(45^{\circ}\) with the x axis with an initial velocity \(\mathrm{v}_0\). The magnitude and direction of the angular momentum of the object with respect to origin, when it reaches at the maximum height, will be [ g is acceleration due to gravity] 2025 Easy
50. 50. Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be ________. 2025 Medium

No questions on this page match these filters. Clear filters