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

50 NEET-AIPMT Chapterwise Topicwise Solutions Physics 7.2 Centre of Mass 1. Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass. The centre of mass of the system from the 5 kg particle is nearly at a distance of (a) 33 cm (b) 50 cm (c) 67 cm (d) 80 cm (NEET 2020) 2. Three masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70 cm. The distance of the centre of mass from the origin is (a) 40 cm (b) 45 cm (c) 50 cm (d) 30 cm (Mains 2012) 3. Two bodies of mass 1 kg and 3 kg have position vectors i j k i j k ^ ^ ^ ^ ^ ^ i + + 2 j k and and − − 3 i 2 j k + , ^ ^ ^ ^ ^ ^ + + 2 and − − 3 2 + , respectively. The centre of mass of this system has a position vector (a) − − 2 i j + k ^ ^ ^ (b) 2 i j 2 k ^ ^ ^ − − (c) − +i j + k ^ ^ ^ (d) − + 2 2 i k ^ ^ (2009) 4. 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 the particles through a distance d, by what distance would be particle of mass m2 move so as to keep the centre of mass of the particles at the original position ? (a) m m m d 1 1 2 + (b) m m d 1 2 (c) d (d) m m d 2 1 (2004) 5. Three identical metal balls, each of radius r are placed touching each other on a horizontal surface such that an equilateral triangle is formed when centres of three balls are joined. The centre of the mass of the system is located at (a) line joining centres of any two balls (b) centre of one of the balls (c) horizontal surface (d) point of intersection of the medians. (1999) 6. The centre of mass of system of particles does not depend on (a) position of the particles (b) relative distances between the particles (c) masses of the particles (d) forces acting on the particle. (1997) 7.3 Motion of Centre of Mass 7. Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weighs 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water the center of mass of the system shifts by (a) 3.0 m (b) 2.3 m (c) zero (d) 0.75 m (2012) 8. 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 (a) 2v (b) zero (c) 1.5v (d) v (2010) 9. A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2 m/s. When the stone reaches the floor, the distance of the man above the floor will be (a) 9.9 m (b) 10.1 m (c) 10 m (d) 20 m (2010) 7.5 Vector Product of Two Vectors 10. Vectors,    A B, and C are such that   A B⋅ = 0 and   A C⋅ = 0 . Then the vector parallel to  A is (a)   A B × (b)   B C+ (c)   B C× (d)   B and C (Karnataka NEET 2013) 11.   A B and are two vectors and q is the angle between them, if | | ( )     A B × = 3 A B⋅ , the value of q is (a) 45° (b) 30° (c) 90° (d) 60° (2007) 12. If the angle between the vectors   A B and is q, the value of the product ( )    B A× ⋅A is equal to (a) BA2 sinq (b) BA2 cosq (c) BA2 sinqcosq (d) zero. (2005, 1989) Systems of Particles and Rotational Motion 7 CHAPTER
Systems of Particles and Rotational Motion 51 13. If | |     A B × = 3A B⋅ then the value of | |   A B + is (a) (A2 + B2 + AB) 1/2 (b) A B 2 2 AB 1 2 3 + +       / (c) A + B (d) A B AB 2 2 1 2 ( + + 3 ) / (2004) 14. The resultant of  A × 0 will be equal to (a) zero (b) A (c) zero vector (d) unit vector. (1992) 7.6 Angular Velocity and its Relation with Linear Velocity 15. What is the value of linear velocity, if  r = − 3 4 i j k + ^ ^ ^ and  ω = 5 6 i − +j 6k ^ ^ ^ ? (a) 4 1 i 3 6 j k ^ ^ ^ − + (b) 18 i 13 j 2k ^ ^ ^ + − (c) 6 2 i j 3k ^ ^ ^ + − (d) 6 2 i j 8k ^ ^ ^ − + (1999) 7.7 Torque and Angular Momentum 16. Find the torque about the origin when a force of 3 j ^ N acts on a particle whose position vector is 2k ^ m . (a) 6 i ^ N m (b) 6 j ^ N m (c) −6 i ^ N m (d) 6k ^ N m (NEET 2020) 17. The moment of the force,  F = + 4 5 i j − 6k ^ ^ ^ at (2, 0, –3), about the point (2, –2, –2), is given by (a) − − 8 4 i j − 7 k ^ ^ ^ (b) − − 4i j − 8k    (c) − − 7 8 i j − 4 k ^ ^ ^ (d) − − 7 4 i j − 8k ^ ^ ^ (NEET 2018) 18. A force  F = + α i j k + ^ ^ ^ 3 6 is acting at a point  r = − 2 6 i j −12k ^ ^ ^ . The value of a for which angular momentum about origin is conserved is (a) zero (b) 1 (c) –1 (d) 2 (2015) 19. A mass m moves in a circle on a smooth horizontal plane with velocity v0 at a radius R0. The mass is attached to a string which passes through a smooth hole in the plane as shown. The tension in the string is increased gradually and finally m moves in a circle of radius R0 2 . The final value of the kinetic energy is (a) 2 0 2 mv (b) 1 2 0 2 mv (c) mv0 2 (d) 1 4 0 2 mv (2015 Cancelled) 20. When a mass is rotating in a plane about a fixed point, its angular momentum is directed along (a) a line perpendicular to the plane of rotation (b) the line making an angle of 45° to the plane of rotation (c) the radius (d) the tangent to the orbit. (2012) 21. A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will (a) decrease by a factor of 2 (b) remain constant (c) increase by a factor of 2 (d) increase by a factor of 4 (Mains 2011) 22. If  F is the force acting on a particle having position vector   r and τ be the torque of this force about the origin, then (a)     r ⋅ >τ 0 and F ⋅ <τ 0 (b)     r ⋅ =τ 0 and F ⋅ =τ 0 (c)     r ⋅ =τ 0 and F ⋅ ≠τ 0 (d)     r ⋅ ≠τ 0 and F ⋅ =τ 0 (2009) 23. A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin O is LA when it is at A and LB when it is at B, then (a) LA = LB (b) the relationship between LA and LB depends upon the slope of the line AB (c) LA < LB (d) LA > LB (2007) 24. Find the torque of a force  F = −3 i+ +j k5 ^ ^ ^ acting at the point  r = + 7 3 i j k + ^ ^ ^ . (a) − + 21 4 i j + 4 k ^ ^ ^ (b) − + 14 i 34 j −16k ^ ^ ^ (c) 14 i 38 j 16k ^ ^ ^ − + (d) 4 4 i j 6k ^ ^ ^ + + (1997) 25. What is the torque of the force  F = − 2 3 i j k + 4 ^ ^ ^ N acting at the point  r = + 3 2 i j k + 3 ^ ^ ^ m about origin? (a) − + 6 6 i j −12k ^ ^ ^ (b) − + 17 i 6 1 j + 3k ^ ^ ^ (c) 6 6 i j 12k ^ ^ ^ − + (d) 17 i 6 1 j 3k ^ ^ ^ − − (1995) 26. A particle of mass m = 5 is moving with a uniform speed v = 3 2 in the XOY plane along the line y = x + 4. The magnitude of the angular momentum of the particle about the origin is (a) 60 units (b) 40 2 units (c) zero (d) 7.5 units (1991) 7.8 Equilibrium of a Rigid Body 27. Which of the following statements are correct? (1) Centre of mass of a body always coincides with the centre of gravity of the body. (2) Centre of mass of a body is the point at which the total gravitational torque on the body is zero. (3) A couple on a body produces both translational and rotational motion in a body. (4) Mechanical advantage greater than one means that small effort can be used to lift a large load. EduHulk.COM