Title 31. Rotational Motion Med 12.pdf ✅

1. If angular displacement of a particle moving on a curved path be given as,  = 1.5 t + 2t2 , where t is in sec, the angular velocity at t = 2 sec, will be (a) 1.5 (b) 2.5 (c) 9.5 (d) 8.5 2. A wheel starts rotating from rest (with constant ) and attains an angular velocity of 60 rad/sec in 5 seconds. The total angular displacement in radians will be (a) 60 (b) 80 (c) 100 (d) 150 3. All the particles of a rigid body in a rotatory motion have axis of rotation: (a) Passing from any point inside the object (b) Passing from any point outside the object (c) Passing from any point (d) Passing from centre of mass of object 4. A wheel has angular acceleration of 3.0 rad/s2 and an initial angular speed of 2.0 rad/s. In a time of 2s it has rotated through an angle (in radian) of (a) 6 (b) 10 (c) 12 (d) 4 5. A fan is running at 3000 rpm. It is switched off. It comes to rest by uniformly decreasing its angular speed in 10 seconds. The total number of revolution in this period. (a) 150 (b) 250 (c) 350 (d) 300 6. A block hangs from a string wrapped on a disc of radius 20 cm free to rotate about its axis which is fixed in a horizontal position. If the angular speed of the disc is 10 rad/s at some instant, with what speed is the block going down at that instant ? (a) 4 m/s (b) 3 m/s (c) 2 m/s (d) 5 m/s 7. A sphere is rotating about a diameter. (a) The particle on the surface of the sphere do not have any linear acceleration (b) The particles on the diameter mentioned above do not have any linear acceleration (c) Different particles on the surface have different angular speeds. (d) All the particles on the surface have same linear speed 8. A stone of mass 4kg is whirled in a horizontal circle of radius 1m and makes 2 rev/sec. The moment of inertia of the stone about the axis of rotation is (a) 64 kg × m2 (b) 4 kg × m2 (c) 16 kg × m2 (d) 1 kg × m2 9. Two spheres of same mass and radius are in contact with each other. If the moment of inertia of a sphere about its diameter is I, then the moment of inertia of both the spheres about the tangent at their common point would be (a) 3 I (b) 7I (c) 4 I (d) 5 I 10. From the theorem of perpendicular axes. If the lamina is in X- Y plane (a) I x – I y = I z (b) I x + I z = I y (c) I x + I y = I z (d) I y + I z = I x 11. The moment of inertia of a body depends upon (a) mass only (b) angular velocity only (c) distribution of particles only (d) mass and distribution of mass about the axis 12. A wheel of mass 10 kg has a moment of inertia of 160 kg m2 about its own axis, the radius of gyration will be (a) 10 m (b) 8 m (c) 6 m (d) 4 m 13. Analogue of mass in rotaional motion is (a) Moment of inertia (b) Angular momentum (c) Torque (d) None of these 14. The moment of inertia of a uniform ring of mass M and radius r about a tangent lying in its own plane is (a) 2Mr2 (b) 3 2 Mr2 (c) Mr2 (d) 1 2 Mr2
15. Three rings each of mass M and radius R are arranged as shown in the figure. The moment of inertia of the system about YY’ will be (a) 3 MR2 (b) 3 2 MR2 (c) 5 MR2 (d) 7 2 MR2 16. Radius of gyration of a body depends on (a) Mass and size of body (b) Mass distribution and axis of rotation (c) Size of body (d) Mass of body 17. The moment of inertia of body comes into play (a) In motion along a curved path (b) In linear motion (c) In rotational motion (d) None of the above 18. Moment of inertia of a ring of mass M and radius R about an axis passing through the centre and perpendicular to the plane is (a) 1/2 MR2 (b) MR2 (c) 1/4 MR2 (d) 3/4 MR2 19. The moment of inertia of a straight thin rod of mass M and length I about an axis perpendicular to its length and passing through its one end, is (a) Ml2 /12 (b) Ml2 /3 (c) Ml2 /2 (d) Ml2 20. Three rods each of length L and mass M are placed along X. Yand Z axes in such a way that one end of each of the rod is at the origin. The moment of inertia of this system about Z axis is (a) 2 2ML 3 (b) 2 4ML 3 (c) 2 5ML 3 (d) 2 ML 3 21. Three point masses each of mass m are placed at the corners of an equilateral triangle of side ‘a’. Then the moment of inertia of this system about an axis passing along one side of the triangle is (a) ma2 (b) 3 ma2 (c) 3/4 ma2 (d) 2/3 ma2 22. The moment of inertia of a uniform thin rod of length L and mass M about an axis passing through a point at a distance of L/3 on the rod from one of its ends and perpendicular to the rod is (a) 2 7ML 48 (b) 2 ML 9 (c) 2 ML 12 (d) 2 ML 3 23. Two rings have their moments of inertia in the ratio 2 : 1 and their diameters are in the ratio 2 : 1. The ratio of their masses will be (a) 2 : 1 (b) 1 : 2 (c) 1 : 4 (d) 1 : 1 24. Four thin rods of same mass M and same length l, form a square as shown in figure. Moment of inertia of this system about an axis through centre O and perpendicular to its plane is (a) 4 2 M 3 l (b) 2 M 3 l (c) 2 M 6 l (d) 2 2 M 3 l 25. Two spheres each of mass M and radius R/2 are connected with a massless rod of length 2R as shown in the-figure. What will be the moment of inertia of the -system about an axis passing through the centre of one of the spheres and perpendicular to l l l l O
the rod (a) 21 2 MR 5 (b) 2 2 MR 5 (c) 5 2 MR 2 (d) 5 2 MR 21 26. The moment of inertia of a disc of mass M and radius R about a tangent to its rim in its plane is : (a) 2 3 MR2 (b) 3 2 MR2 (c) 4 5 MR2 (d) 5 4 MR2 27. lf the moment of inertia of a disc about an axis tangential and parallel to its surface be I, then what will be the moment of inertia about the axis tangential but perpendicular to the surface (a) I 6 5 (b) I 3 4 (c) I 3 2 (d) I 5 4 28. The moment of inertia of a sphere of mass M and radius R about an axis passing through its centre is 2 2 MR 5 . The radius of gyration of the sphere about a parallel axis to the above and tangent to the sphere is (a) 7 R 5 (b) 3 R 5 (c) 7 R 5         (d) 3 R 5         29. Four particles each of mass m are placed at the corners of a square of side length l. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is (a) 2 l (b) 2 l (c) l (d) ( 2) l 30. One circular ring and one circular disc, both are having the same mass and radius. The ratio of their moments of inertia about the axes passing through their centres and perpendicular to their planes. will be (a) 1 : 1 (b) 2 : 1 (c) 1: 2 (d) 4 : 1 31. The radius of gyration of a disc of mass 100 g and radius 5 cm about an axis passing through centre of gravity and perpendicular to the plane is (a) 3.54 cm (b) 1.54 cm (c) 4.54 cm (d) 2.5 cm 32. The moment of inertia of a solid sphere about its tangential axis will be : (a) 2 5 MR2 (b) 7 5 MR2 (c) 5 3 MR2 (d) 2 3 MR2 33. The moment of inertia in rotational motion will be equivalent to ...... as in linear motion : (a) mass (b) velocity (c) momentum (d) force 34. Out of the given bodies ( of same mass) for which the moment of inertia will be maximum about the axis passing through its centre of gravity and perpendicular to its plane? (a) Disc of radius a (b) Ring of radius a (c) Square lamina of side 2a (d) Four rods of length 2a making a square 35. Five particles of mass 2 kg are attached to the rim of a circular disc of radius 0.1 m and negligible mass. Moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to its plane is : (a) 1 kg m2 (b) 0.1 kg m2 (c) 2 kg m2 (d) 0.2 kg m2 36. If the moment of inertia of a disc about an axis tangential and parallel to its surface be I,, then what will be the moment of inertia about the axis tangential but perpendicular to the surface ? 2R R/2 P M Y M Q Y’
(a) 6 5  (b) 3 4  (c) 3 2  (d) 5 4  37. The moment of inertia of a uniform semicircular wire of mass M and radius R about a line perpendicular to the plane of the wire through the centre is (a) MR2 (b) 1 2 MR2 (c) 1 4 MR2 (d) 2 5 MR2 38. Let IA and IB be moments of inertia of a body about two axes A and B respectively, The axis A passes through the centre of mass of the body but B does not. (a) IA < IB (b) If IA < IB , the axes are parallel. (c) If the axes are parallel, IA < IB (d) If the axes are not parallel, IA  I B . 39. A thin rod of length L and mass M is bend at the middle point O as shown in figure. Consider an axis passing through two middle point O and perpendicular to the plane of the bent rod. Then moment of inertia about this axis is : (a) 2/3 mL2 (b) 1/3 mL2 (c) 1/12 mL2 (d) 1/24 mL2 40. The moment of inertia of a uniform circular disc about its diameter is 200 gm cm2 . Then its moment of inertia about an axis passing through its center and perpendicular to its circular face is (a) 100 gm cm2 (b) 200 gm cm2 (c) 400 gm cm2 (d) 1000 gm cm2 41. Moment of inertia of a uniform disc about tangential axis OO lying in the plan of the disc ,is: (a) 2 3 m r 2 (b) 2 mr 2 (c) 2 5 m r 2 (d) 2 5 m r 4 42. Three rings each of mass m and radius r are so placed that they touch each other. The radius of gyration of the system about the axis as shown in the figure is : (a) 6 r 5 (b) 5 r 6 (c) 6 r 7 (d) 7 r 6 43. ABC is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. IAB, IBC, ICA are the moments of inertia of the plate about AB, BC, CA respectively. Which one of the following relations is correct (a)  CA is maximum (b)  AB >  BC (c)  BC >  AB (d)  AB +  BC =  CA 44. A circular disc is to be made using iron and aluminium. To keep its moment of inertia maximum about a geometrical axis, it should be so prepared that :- (a) aluminium at interior and iron surrounds it (b) iron at interior and aluminium surrounds it (c) aluminium and iron layers in alternate order O O¢ m r