Tiêu đề 7. System of Particles and Rotational Motion.pdf ✅

1. Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are v and 2v at any instant, then the speed of centre of mass of the system will be :- (1) v (2) 2v (3) Zero (4) 1.5 v 2. A circular disk of moment of inertia It is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed i. Another disk of moment of inertia Ib is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed f. The energy lost by the initially rotating disc to friction is :- 3. The centre of mass of a body : (1) Lies always outside the body (2) May lie within, outside or on the surface of the body (3) Lies always inside the body (4) Lies always on the surface of the body 4. The centre of mass of two masses m & m' moves by distance 5 x when mass m is moved by distance x and m' is kept fixed. The ratio m ' m is: - (1) 2 (2) 4 (3) 1/4 (4) None of these 5. Find the torque of a force ˆ ˆ ˆ F i j k = − + + 3 5 acting at the point ˆ ˆ ˆ r i j k = + + 7 3 with respect to origin :- 6. A wheel is rotating about an axis through its centre at 720 rpm. It is acted on by a constant torque opposing its motion for 8 seconds to bring it to rest finally. The value of torque (in N-m) is :- (1) 48 (2) 72 (3) 96 (4) 120 7. A uniform rod of length L is free to rotate in a vertical plane about a fixed horizontal axis through B. The rod begins rotating from rest from its unstable equilibrium position. When it has turned through an angle  its angular velocity  is given as :- 8. Two wheels are connected by a belt. The radius of larger wheel is three times that of the smaller one. What is the ratio of the rotational inertia of larger wheel to the smaller wheel, when both wheels have same angular momentum ? (1) 3 (2) 6 (3) 9 (4) 12 9. A disc is rolling on an inclined plane. What is the ratio of its rotational KE to the total KE - (1) 1 : 3 (2) 3 : 1 (3) 1 : 2 (4) 2 : 1 10 . A uniform solid sphere of mass m and radius r rolls without slipping down a inclined plane, inclined at an angle 45° to the horizontal. Find the magnitude of frictional coefficient at which slipping is absent– 11. A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its end with a uniform angular System of Particles and Rotational Motion
velocity . The force exerted by the liquid at the other end is– 12. We have two spheres one of which is hollow and the other solid. They have identical masses and moment of inertia about their respectively diameters. The ratio of their radius is given by:– (1) 5 : 7 (2) 3 : 5 (3) 3 : 5 (4) 3 : 7 13. Two particles A and B initially at rest move towards each other under a mutual force of attraction. At the inst ant when velocity of A is v and that of B is 2v, the velocity of centre of mass of the system : (1) v (2) 2v (3) 3v (4) Zero 14. A particle of mass m describes a circle of radius r. The centripetal acceleration of the particle is 4/r2 . What will be the momentum of the particle ? 15. The position of a particle is given by: ˆ ˆ ˆ r i j k = + − 2 and its linear momentum is given by: ˆ ˆ ˆ p i j k = + − 3 4 2 . Then its angular momentum, about the origin is perpendicular to – (1) YZ-plane (2) z-axis (3) y-axis (4) x-axis 16. Five masses each of 2 kg are placed on a horizontal circular disc, which can be rotated about a vertical axis passing through its centre and all the masses be equidistant from the axis and at a distance of 10 cm from it. The moment of inertia of the whole system (in gm-cm2 ) is: (Assume disc is of negligible mass) (1) 105 (2) 104 (3) 106 (4) 108 17. A uniform rod of length 1 m is bent at its mid-point to make 90o angle. The distance of the centre of mass from the centre of the rod is :- (1) 36.1 cm (2) 25.2 cm (3) 17.7 cm (4) zero 18. A T shaped object with dimensions shown in the figure, is lying a smooth floor. A force ' ' F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C:- 19. Four masses are fixed on a mass less rod as shown in Fig. The moment of inertia about the axis P is about : (1) 2 kg m2 (2) 1 kg m2 (3) 0.5 kg m2 (4) 0.3 kg m2 20. Four particles, each of mass m, are arranged at the corners of a mass less square of side 'a'. Moment of inertia of system about a diagonal is : 21. A circular ring of mass 6 kg and radius a is placed such that its centre lies at the origin. Two particles of mass 2 kg each are placed at the intersecting points of the circle with
+ ve x-axis and +vey-axis. Then the angle made by the position vector of centre of mass of entire system with x-axis is:- (1) 45° (2) 60° (3) tan–1 (4/5) (4) 30° 22. Two spheres each of mass M and radius R/2 are connected with a mass less rod of length 2R as shown in the figure. The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rods - (1) 21 2 5 MR (2) 2 2 5 MR (3) 5 2 2 MR (4) 5 2 21 MR A. If both Assertion & Reason are True & The Reason is a correct explanation of the Assertion. B. If both Assertion & Reason are True but Reason is not a correct explanation of the Assertion. C. If Assertion is True but the Reason is False. D. If both Assertion & Reason are False. 23. Assertion :- The centre of mass of system of n particles is the weighted average of the position vector of the n particles making up the system. Reason :- The position of the centre of mass of a system is independent of coordinate system. (1) A (2) B (3) C (4) D 24. A circular disc X of radius R is made from an iron plate of thickness t and another disc Y of radius4R is made from an iron plate of thickness t/4.Then the relation between the moment of inertia IX and IY is :- (1) IY = 32 IX (2) IY = 16IX (3) IY = IX (4) IY = 64 IX 25. Consider the following two statements :- (A) Linear momentum of a system of particles is zero. (B) Kinetic energy of a system of particles is zero. Then :- (1) A does not imply B and B does not imply A (2) A implies B but B does not imply A (3) A does not imply B but B implies A (4) A implies B and B implies A 26. Consider a uniform square plat of side ‘a’ and mass ‘m’ the moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is 27. A bob of mass m attached to an inextensible string of length is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed  rad/s about the vertical. About the point of suspension : (1) Angular momentum changes in direction but not in magnitude (2) Angular momentum changes both in direction and magnitude (3) Angular momentum is conserved (4) Angular momentum changes in magnitude but not in direction. 28. A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is R from the centre of the bigger disc. The value of is : -
29. A mass ‘m’ is supported by a mass less string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release? 30. A constant torque acting on a uniform circular wheel changes its angular momentum from L0 to 4L0 in 4 s. The magnitude of this torque is (1) (3/4)L0 (2) L0 (3) 4L0 (4) 12L0 31. A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass 1 3 M and body C of mass 2 3 M . The centre of mass of bodies B and C taken together shifts compared to that of body A towards :- (1) body C 2) body B (3) depends on height of breaking (4) Does not shift 32. Consider a uniform square plate of side a and mass m. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is :- (1) 5 2 6 ma (2) 1 2 12 ma (3) 7 2 12 ma (4) 2 2 3 ma 33. Two solids spheres of iron have radii in The ratio 1 : 2. Their moments of inertia will be in the ratio (1) 1 : 4 (2) 1 : 8 (3) 1 : 16 (4) 1 : 32 34. A car changes speed from 18 km/h to 36 km/h in 5 s. The diameter of its wheel is 0.8 m. The angular acceleration of the wheel is (1) 1 rad/s2 (2) 0.8 rad/s2 (3) 2.5 rad/s2 (4) 1.8 rad/s2 35. A body is hinged about any point on the x- axis and its moment of inertia I is given as I = 2x2 – 12x + 27 value of x co-ordinate of centre of mass will be :- (1) x = 2 (2) x = 3 (3) x = 0 (4) x = 1 36. A projectile is fired at a speed of 100 m/sec at an angle of 37° above the horizontal. At the highest point, the projectile breaks into two parts of mass ratio 1:3, the smaller coming to rest. Then the distance of heavier part from the launching point is : (1) 480 m (2) 960 m (3) 1120 m (4) 1440 m 37. The distance of the centre of mass of the T-shaped plate from O is : (1) 7 m (2) 2.7 m (3) 4 m (4) 1 m 38. The moment of inertia of a uniform rod of length2 and mass m about an axis xx'