Tiêu đề 7.SYSTEM OF PARTICLES AND ROTATIONAL MOTION - Questions.pdf ✅

7.SYSTEM OF PARTICLES AND ROTATIONAL MOTION (1.)When the angle of inclination of an inclined plane is θ, an object slides down with uniform velocity. If the same object is pushed up with a initial velocity u on the same inclined plane; it goes up the plane and stops at a certain distance on the plane. Thereafter the body (a.) Slides down the inclined plane and reaches the ground with velocity u. (b.) Slides down the inclined plane and reaches the ground with velocity less than u. (c.) Slides down the inclined plane and reaches the ground with velocity greater than u. (d.) Stays at rest on the inclined plane and will not slide down. (2.)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 MR 2 (b.) 3 2 MR 2 (c.) 5 MR 2 (d.) 7 2 MR 2 (3.)The speed of a homogeneous solid sphere after rolling down an inclined plane of vertical height h, form rest without sliding, is (a.) √ 10 7 gh (b.) √gh (c.) √ 6 5 gh (d.) √ 4 3 gh (4.)A bullet of mass 5g moving with a velocity 10 ms −1 strikes a stationary body of mass 955g and enters it. The percentage loss of kinetic energy of the bullet is (a.) 85 (b.) 0.05 (c.) 99.5 (d.) None of the above (5.)Three point masses m1, m2, m3 are located at the vertices of an equilateral triangle of length ‘a’. The moment of inertia of the system about an axis along the altitude of the triangle passing through m1 is (a.) (m2 + m3 ) a 2 4 (b.) (m1 + m2 + m3 )a 2 (c.) (m1 + m2 ) a 2 4 (d.) (m2 + m3 )a 2 (6.) A wheel rotates with a constant angular velocity of 300 rpm. The angle through which the wheel rotates in 1 s is (a.) π rad (b.) 5π rad (c.) 10π rad (d.) 20π rad (7.)Analogue of mass in rotational motion is (a.) Moment of inertia (b.) Angular momentum (c.) Torque (d.) None of these (8.)In a metallic triangular sheet ABC, AB = BC = 1. If M is its moment of inertia about AC. (a.) Ml 2 4 (b.) Ml 2 12 (c.) Ml 2 6 (d.) Ml 2 18 (9.)A thin uniform rod mass m and length l is hinged at the lower end to a level floor and stands vertically. It is now allowed to fall, then its upper end will strike the floor with a velocity given by (a.) √2gl (b.) √3gl (c.) √5gl (d.) √mgl (10.)One quarter of the disc of mass m is removed. If r be the radius of the disc, the new moment of inertia is (a.) 3 2 mr 2 (b.) mr 2 2 (c.) 3 8 mr 2 (d.) None of these (11.)A ball of mass m1 is a moving with velocity v. It collides head on elastically with a stationary ball of Y Y
mass m2. The velocity of ball becomes v/3 after collision. Then the value of the ratio m2 m1 is (a.) 1 (b.) 2 (c.) 3 (d.) 4 (12.)A cart of mass M is tied by one end of a massless rope of length 10 m. The other end of the rope is in the hands of a man of mass M. The entire system is on a smooth horizontal surface. The man is at x = 0 and the cart at x = 10m. If the man pulls the cart by the rope, the man and the cart will meet at the point (a.) x = 0 (b.) x = 5m (c.) x = 10m (d.) They will never meet (13.)The radius of gyration of a body about an axis at a distance 6 cm from its centre of mass is 10 cm. Then its radius of gyration about a parallel axis through its centre of mass will be (a.) 80 cm (b.) 8 cm (c.) 0.8 cm (d.) 80 cm (14.)A particle of mass 1 kg is projected with an initial velocity 10 ms−1 at an angle of projection 450 with the horizontal. The average torque acting on the projectile, between the time at which it is projected and the time at which it strikes the ground, about the point of projection in newton- metre is (a.) 25 (b.) 50 (c.) 75 (d.) 100 (15.)A small object of mass m is attached to a light string which passes through a hollow tube. The tube is hold by one hand and the string by the other. The object is set into rotation in a circle of radius R and velocity v. The string is then pulled down, shortening the radius of path of r. What is conserved (a.) Angular momentum (b.) Linear momentum (c.) Kinetic energy (d.) None of the above (16.)A thin rod of length ′L′ lying along the x-axis with its ends at x = 0 and x = L. Its linear density (mass/length) varies with x as k ( x L ) n , where n can be zero or any positive number. If the position xcm of the centre of mass of the rod is plotted against ′n′, which of the following graphs best approximates the dependence of xcm on n (a.) (b.) (c.) (d.) (17.)The distance between the centres of carbon and oxygen atoms in the carbon monoxide molecule is 1.130 Å. Locate the centre of mass of the molecule relative to the carbon atom. (a.) 5.428 Å (b.) 1.130 Å (c.) 0.6457 Å (d.) 0.3260 Å (18.)If the angular momentum of a rotating body about a fixed axis is increased by 10%. Its kinetic energy will be increased by (a.) 10% (b.) 20% (c.) 21% (d.) 5% (19.)Consider a system of two particles having masses m1 and m2. If the particle of mass m1 is pushed towards the centre of mass of particles through a distance d, by what distance would be particle of mass m2 move so as to keep the centre of mass of particles at the original position (a.) m1 m1+m2 d (b.) m1 m2 d (c.) d (d.) m2 m1 d (20.)Four particles of masses m, 2m, 3m and 4m are arranged at the corners of a parallelogram with each inside equal to a and one of the angle between two adjacent sides is 60°. The parallelogram lies in the x-y plane with mass m at the origin and 4m on the x-axis. The centre of mass of the arrangement will be located at (a.) ( √3 2 a, 0.95a)
(b.) (0.95a, √3 4 a) (c.) ( 3a 4 , a 2 ) (d.) ( a 2 , 3a 4 ) (21.)A particle is projected with a speed v at 450 with the horizontal. The magnitude of angular momentum of the projectille about the point of projection when the particle is at its maximum height h is (a.) Zero (b.) mvh 2 √2 (c.) mv 2h √2 (d.) mv2h √2 (22.)Two solid spheres (A and B) are made of metals of different densities ρA and ρB respectively. If their masses are equal, the ratio of their moments of inertia (IB/IA ) about their respective diameters is (a.) ( ρB ρA ) 2/3 (b.) ( ρA ρB ) 2/3 (c.) ρA ρB (d.) ρB ρA (23.)A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now, the platform is given an angular velocity ω0. When the tortoise moves along a chord of the platform with a constant velocity (with respect to the platform), the angular velocity of the platform ω(t) will vary with time t as (a.) (b.) (c.) (d.) (24.)Four point masses P,Q, R and S with respective masses 1 kg, 1 kg, 2 kg form the corners of a square of side a. The center of mass of the system will be farthest from (a.) P only (b.) R and S (c.) R only (d.) P and Q (25.)Two perfectly elastic objects A and B of identical mass are moving with velocities 15 ms −1 and 10 ms −1 respectively, collide along the direction of line joining them. Their velocities after collision are respectively (a.) 10 ms −1 ,15 ms −1 (b.) 20 ms −1 , 5 ms −1 (c.) 0 ms −1 , 25ms −1 (d.) 5 ms −1 , 20ms −1 (26.)The moment of inertia of a solid cylinder of mass M and radius R about a line parallel to the axis of the cylinder and lying on the surface of the cylinder is (a.) 2 5 MR 2 (b.) 3 5 MR 2 (c.) 3 2 MR 2 (d.) 5 2 MR 2 (27.)In the absence of external torque for a body revolving about any axis, the quantity that remains constant is (a.) Kinetic energy (b.) Potential energy (c.) Linear momentum (d.) Angular momentum (28.)Very thin ring of radius R is rotated about its centre. It’s radius will (a.) Increase (b.) Decrease (c.) Change depends on the material (d.) None of these (29.)A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child stretches his arms so that the moment of inertia of the system doubles. The kinetic energy of the system now is (a.) 2K (b.) K 2 (t) O t (t) O t (t) O t (t) O t
(c.) K 4 (d.) 4K (30.)The radius of gyration of a disc of mass 50 g and radius 2.5 cm, about an axis passing through its centre of gravity and perpendicular to the plane, is (a.) 0.52 cm (b.) 1.76 cm (c.) 3.54 cm (d.) 6.54 cm (31.)A symmetrical body is rotating about its axis of symmetry, its moment of inertia about the axis of rotation being 4 kg-m2 and its rate of rotation 2 rev/s. The angular momentum is (a.) 1.257 kg m2 s −1 (b.) 12.57 kg m2 s −1 (c.) 13.57 kg m2 s −1 (d.) 20 kg m2 s −1 (32.)A wheel has a speed of 1200 revolutions per minute and is made to slow down at a rate of 4 radians/s 2 . The number of revolutions it makes before coming to rest is (a.) 143 (b.) 272 (c.) 314 (d.) 722 (33.)A solid cylinder (SC) a hollow cylinder (HC) and a solid sphere (S) of the same mass and radius are released simultaneously from the same height of incline. The order in which these bodies reach the bottom of the incline is (a.) SC, HC, S (b.) SC, S, HC (c.) S, SC, HC (d.) HC, SC, S (34.)A wheel rotates with a constant acceleration of 2.0 radian/sec2 . If the wheel starts from rest the number of revolutions it makes in the first ten seconds will be approximately (a.) 8 (b.) 16 (c.) 24 (d.) 32 (35.)A sphere of mass m and radius r rolls on a horizontal plane without slipping with the speed u. Now if it rolls up vertically, the maximum height it would attain will be (a.) 3u 2 /4g (b.) 5u 2 /2g (c.) 7u 2 /10g (d.) u 2 /2g (36.)A particle with position vector r has a linear momentum p. Which of the following statements is true in respect of its angular momentum L about the origin (a.) L acts along p (b.) L acts along r (c.) L is maximum when p and r are parallel (d.) L is maximum when p is perpendicular to r (37.)A disc is rolling (without slipping) on a horizontal surface. C is its centre and Q and P are two points equidistant from C. Let vP, vQ and vC be the magnitude of velocities of points P,Q and C respectively, then (a.) vQ > vC > vP (b.) vQ < vC < vP (c.) vQ = vP, vC = vP 2 (d.) vQ < vC > vP (38.)A bomb at rest explodes in air into two equal fragments. If one of the fragments is moving vertically upwards with velocity v0, then the other fragment will move (a.) Vertically up with velocity v0 (b.) Vertically down with velocity v0 (c.) In arbitrary direction with velocity v0 (d.) Horizontally with velocity v0 (39.)The moment of inertia of wheel about the axis of rotation is 3.0 MKS units. Its kinetic energy will be 600 J if period of rotation is (a.) 0.05 s (b.) 0.314 s (c.) 3.18 s (d.) 20 s (40.)The moment of inertia of a sphere of mass M and radius R about an axis passing through its centre is 2 5 MR 2 . The radius of gyration of the sphere about a parallel axis to the above and tangent to the sphere is (a.) 7 5 R (b.) 3 5 R (c.) (√ 7 5 )R (d.) (√ 3 5 ) R (41.)A particle of mass m = 5 units is moving with a uniform speed v = 3√2 units in the XOY plane along the straight line Y = X + 4. The magnitude of the angular momentum about origin is (a.) Zero (b.) 60 units (c.) 75 units (d.) 40√2 units P C Q