Title 5. Laws of Motion.pdf ✅

1. An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the insect and the surface is 1/3. If the line joining the centre of the hemispherical surface to the insect makes an angle  with the vertical, the maximum possible value of  is given by (1) cot = 3 (2) tan  = 3 (3) sec = 3 (4) cosec  = 3 2. An object of mass 5 kg is attached to the hook of a spring balance and the balance is suspended vertically from the roof of a lift. The reading on the spring balance when the lift is going up with an acceleration of 0.25ms–2 is :(Take g = 10 m/s2 ) (1) 51.25 N (2) 48.75 N (3) 52.75 N (4) 47.25 N 3. Minimum horizontal Force required to move a mass of 1 kg at rest on a horizontal rough plane (μ = 0.1 and g=9.8 m/s2 ) is :- (1) 0.98 N (2) 0.49 N (3) 9.8 N (4) 4.9 N 4. System shown in figure is released from rest. Pulley and spring are massless and the friction is absent everywhere. The speed of 5 kg block, when 2 kg block leaves the contact with ground is : (take force constant of the spring K = 40 N/m and g = 10 m/s2 ) 5 . Two masses of 1 kg and 5 kg are attached to the ends of a massless string passing over a pulley of negligible weight. The pulley itself is attached to a light spring balance as shown in figure. The masses start moving during this interval; the reading of spring balance will be– (1) More than 6 kg. (2) Less than 6 kg. (3) Equal t o 6 kg. (4) None of t he above 6 . A block of mass m is lying on an inclined plane. The coefficient of friction between the plane and the block is . The force (F1) required t o move t he block up the inclined plane will be– (1) mg sin + mg cos (2) mg cos – mg si n (3) mg sin – mg cos (4) mg cos + mg sin 7 . The tension T in the string shown in figure is– (1) Zero (2) 50 N (3) 35 3N (4) ( 3 1 50 − ) N 8. In the arrangement shown in figure, pulley is smooth and massless and all t he strings are light let F2 be the force exerted on the pulley in case (i) and F1 the force in case (ii). Then Laws of Motion
9 . The limiting friction between two bodies in contact is independent of– (1) Nature of the surface in content (2) The area of surfaces in contact (3) Normal react ion between the surfaces (4) The material of the bodies 10. For the given figure, if block remains in equilibrium position then find frictional force between block and wall : (1)100 N (2) 50 N (3) 200 N (4) None 11. A horizontal force F is applied to a frictionless pulley of mass m2. The horizontal surface is smooth. Acceleration of the block of mass (m1) is 12. A particle of mass m is moving in a horizontal circle of radius r under centripetal force equal to 2 , K r − where K is a constant. The total energy of the particle is :- 13. A block Q of mass M is placed on a horizontal frictionless surface AB and a body P of mass m is released on its frictionless slope. As P slides by a length L on this slope of inclination , the block Q would slide by a distance :- 14. In the first second of its flight, rocket ejects1/60 of its mass with a velocity of 2400 m/s–1 . The acceleration of the rocket is:- (1) 19.6 ms–2 (2) 30.2 ms–2 (3) 40 ms–2 (4) 49.8 ms–2 15. Two small particles of equal masses start moving in opposite direction from a point A in a horizontal circular orbit. Their tangential velocities are v and2v, respectively, as shown in the figure. Between collisions, the particles move with constant speeds, After making how many elastic collisions, other than that at A, these two particles will again reach the point A:- (1) 4 (2) 3 (3) 2 (4) 1 16. A particle of mass m moving with a velocity u makes an elastic one dimensional collision with a stationary particle of mass m establishing a contact
with it for extremely small time T. Their force of contact increases from zero to F0 linearly in time , 4 T remains constant for a further time , 2 T and decreases linearly from F0 to zero in further time , 4 T as shown. The magnitude possessed by F0is:- 17. Two fixed frictionless inclined planes making an angle 30° and 60° with the vertical are shown in the figure. Two blocks A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B? (1) 4.9 ms–2 in vertical direction. (2) 4.9 ms–2 in horizontal direction (3) 9.8 ms–2 in vertical direction (4) Zero 18. One end of massless rope, which passes over a massless and frictionless pulley P is tied to a hook C while the other end is free. Maximum tension that the rope can bear is 840 N. With what value of maximum safe acceleration (in ms–2) can a man of 60 kg climb on the rope? (1) 16 (2) 6 (3) 4 (4) 8 19. A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves0.2 m while applying the force and the ball goes upto 2m height further, find the magnitude of the force. Consider g = 10 m/s2 : (1) 4 N (2) 16 N (3) 20 N (4) 22 N 20. A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is :- (1) 5 40 4 m/s (2)20 m/s (3)10 m/s (4) 10 30 m/s 21. A rocket which has a mass of 4 3.5 10  kg is blasted upwards with an initial acceleration of10 m/s2. Then the initial thrust of the blast is- (1) 3.5 × 105 N (2) 7.0 × 105 N (3) 14.0 × 105 N (4) 1.75 × 105 N 22. Two particles of equal masses are revolving in circular paths of radii r1 and r2 respectively with the same linear speed. The ratio of their centripetal forces is 23. A person pushes a box kept on a horizontal surface with force of 100 N. In unit vector notation force F can be expressed as ?
24. Three equal weights of mass 2 kg each are hanging on a string passing over a fixed pulley as shown in the figure. What is the tension of the string connecting weights B and C? (1) 1.3kgf (2) 1.3N (3) 3.3 N (4) 19.6N 25. Among the forces in nature, friction can be classified into (1) Electromagnetic (2) Gravitational (3) Nuclear (4) Other weak forces 26. A chain of length L rests on a rough table. If  be the coefficient of friction, the maximum friction of the chain that can hang over the table will be 27. Adjoining figure shows two blocks A and B pushed against the wall with the force F. The wall is smooth but the surface in contact of A and B are rough. Which of the following is true for the system of blocks to be at rest against the wall? (1) F should be more than the weight of A and B (2) F should be equal to the weight of A and B (3) F should be less than the weight of A and B (4) System cannot be in equilibrium 28. An engine pumps water continuously through a hose. Water leaves the hose pipe with velocity v and m is the mass per unit length of water jet. If this jet hits a surface and comes to rest instantaneously, the force on the surface is:- (1) 2 mv (2) 1 2 2 mv (3) 3 mv (4) 1 3 2 mv 29. A wire, which passes through the hole in a small bead is bent in the form of a circle. The wire is fixed vertically on the ground as shown in the figure. The bead in released from the top of the wire and it slides along the wire without friction. As the bead moves from A to B the force it applies on the wire is :- (1) Always radially outward (2) Always radially inward (3) Radially outward initially and radially inward later (4) Radially inward initially and radially outward later 30. A rope is used to lower vertically a block of mass M by a distance x at a constant downward acceleration g/2. The work done by the rope on the block is :- 31. A block rests on a horizontal surface and a man pulls it with a 10N force. Rank the situation shown below according to the magnitude of the normal force exerted by the surface on the block, least to maximum