Title 5. Laws of Motion .pdf ✅

26 (a) 15 kg (b) 20 kg (c) 10 kg (d) 5 kg (1996) 13. A force vector applied on a mass is represented as  F = − 6 8 i j +10k ^ ^ ^ and accelerates with 1 m/s2 . What will be the mass of the body? (a) 10 kg (b) 20 kg (c) 10 2 kg (d) 2 10 kg (1996) 14. In a rocket, fuel burns at the rate of 1 kg/s. This fuel is ejected from the rocket with a velocity of 60 km/s. This exerts a force on the rocket equal to (a) 6000 N (b) 60000 N (c) 60 N (d) 600 N (1994) 15. A satellite in force free space sweeps stationary interplanetary dust at a rate of dM/dt = av, where M is mass and v is the speed of satellite and a is a constant. The acceleration of satellite is (a) − αv M 2 2 (b) –av2 (c) − 2αv M 2 (d) − αv M 2 (1994) 16. A particle of mass m is moving with a uniform velocity v1. It is given an impulse such that its velocity becomes v2. The impulse is equal to (a) m[|v2| – |v1|] (b) 1 2 2 2 1 2 m v[ − v ] (c) m[v1 + v2] (d) m[v2 – v1] (1990) 17. A 600 kg rocket is set for a vertical firing. If the exhaust speed is 1000 m s–1, the mass of the gas ejected per second to supply the thrust needed to overcome the weight of rocket is (a) 117.6 kg s–1 (b) 58.6 kg s–1 (c) 6 kg s–1 (d) 76.4 kg s–1 (1990) 5.6 Newton’s Third Law of Motion 18. A rigid ball of mass m strikes a rigid wall at 60° and gets reflected without loss of speed as shown in the figure. The value of impulse imparted by the wall on the ball will be (a) mV (b) 2 mV (c) mV 2 (d) mV 3 (NEET-II 2016) 19. A body of mass M hits normally a rigid wall with velocity V and bounces back with the same velocity. The impulse experienced by the body is (a) MV (b) 1.5MV (c) 2MV (d) zero (2011) 20. A 0.5 kg ball moving with a speed of 12 m/s strikes a hard wall at an angle of 30° with the wall. It is reflected with the same speed at the same angle. If the ball is in contact with the wall for 0.25 seconds, the average force acting on the wall is (a) 96 N (b) 48 N (c) 24 N (d) 12 N (2006) 21. A body of mass 3 kg hits a wall at an angle of 60° and returns at the same angle. The impact time was 0.2 s. The force exerted on the wall (a) 150 3 N (b) 50 3 N (c) 100 N (d) 75 3 N (2000) 5.7 Conservation of Momentum 22. An object flying in air with velocity (20i 25j 12k)    + − suddenly breaks in two pieces whose masses are in the ratio 1 : 5. The smaller mass flies off with a velocity (100i 35j 8k)    + + . The velocity of the larger piece will be (a) 4 2 i 3 1 j 6k    + − (b) − − 100i 35j − 8k    (c) 20i 15j 80k    + − (d) − − 20i 15j − 80k   . (Odisha NEET 2019) 23. An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 m s–1 and the second part of mass 2 kg moves with 8 m s–1 speed. If the third part flies off with 4 m s–1 speed, then its mass is (a) 7 kg (b) 17 kg (c) 3 kg (d) 5 kg (NEET 2013) 24. A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5 s. Each bullet has a mass of 10 g with a muzzle velocity of 800 m s–1. The final velocity acquired by the person and the average force exerted on the person are (a) – 0.08 m s–1, 16 N (b) – 0.8 m s–1, 8 N (c) – 1.6 m s–1, 16 N (d) – 1.6 m s–1, 8 N (Karnataka NEET 2013) 25. An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, 1 kg first part moving with a velocity of 12 m s–1 and 2 kg second part moving with a velocity 8 m s–1. If the third part flies off with a velocity of 4 m s–1, its mass would be (a) 7 kg (b) 17 kg (c) 3 kg (d) 5 kg (2009) EduHulk.COM
Laws of Motion 27 26. A 1 kg stationary bomb is exploded in three parts having mass 1 : 1 : 3 respectively. Parts having same mass move in perpendicular direction with velocity 30 m/s, then the velocity of bigger part will be (a) 10 2 m/s (b) 10 2 m/s (c) 15 2 m/s (d) 15 2 m/s (2001) 27. A mass of 1 kg is thrown up with a velocity of 100 m/s. After 5 seconds, it explodes into two parts. One part of mass 400 g comes down with a velocity 25 m/s. The velocity of other part is (Take g = 10 m s–2) (a) 40 m/s (b) 80 m/s (c) 100 m/s (d) 60 m/s (2000) 28. A shell, in flight, explodes into four unequal parts. Which of the following is conserved? (a) Potential energy (b) Momentum (c) Kinetic energy (d) Both (a) and (c). (1998) 29. A man fires a bullet of mass 200 g at a speed of 5 m/s. The gun is of one kg mass. By what velocity the gun rebounds backward? (a) 1 m/s (b) 0.01 m/s (c) 0.1 m/s (d) 10 m/s. (1996) 30. A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragments with equal masses fly in mutually perpendicular directions with speeds of 21 m/s. The velocity of heaviest fragment in m/s will be (a) 7 2 (b) 5 2 (c) 3 2 (d) 2 (1989) 5.8 Equilibrium of a Particle 31. A particle moving with velocity  v is acted by three forces shown by the vector triangle PQR. The v e l o c i t y of the particle will (a) change according to the smallest force QR (b) increase (c) decrease (d) remain constant (NEET 2019) 32. Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is (a) 3 4 N 4 N 1 N Y 30° 60° X 2 N (b) 3 N (c) 0.5 N (d) 1.5 N (2008) 5.9 Common Forces in Mechanics 33. Which one of the following statements is incorrect? (a) Rolling friction is smaller than sliding friction. (b) Limiting value of static friction is directly proportional to normal reaction. (c) Frictional force opposes the relative motion. (d) Coefficient of sliding friction has dimensions of length. (NEET 2018) 34. A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30°, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be, respectively (a) 0.5 and 0.6 (b) 0.4 and 0.3 (c) 0.6 and 0.6 (d) 0.6 and 0.5 (2015) 35. A block A of mass m1 rests on a horizontal table. A light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block B of mass m2 is suspended. The coefficient of kinetic friction between the block and the table is mk. When the block A is sliding on the table, the tension in the string is (a) m m g m m 1 2 k 1 2 (1 ) ( ) + + μ (b) m m g m m 1 2 k 1 2 (1 ) ( ) − + μ (c) ( ) ( ) m m g m m 2 k 1 1 2 + + μ (d) ( ) ( ) m m g m m 2 k 1 1 2 − + μ (2015 Cancelled) 36. A system consists of three masses m1, m2 and m3 connected by a string passing over a pulley P. The mass m1 hangs freely and m2 and m3 are on a rough horizontal table (the coefficient of friction = m). The pulley is frictionless and of negligible mass. The downward acceleration of mass m1 is (Assume m1 = m2 = m3 = m) (a) g(1 g ) 9 − μ (b) 2 3 gμ (c) g(1 2 ) 3 − μ (d) g(1 2 ) 2 − μ (2014) 37. The upper half of an inclined plane of inclination q is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by
28 (a) m = 2 tanq (b) m = tanq (c) μ θ = 1 tan (d) μ θ = 2 tan (NEET 2013) 38. A conveyor belt is moving at a constant speed of 2 m s–1. A box is gently dropped on it. The coefficient of friction between them is m = 0.5. The distance that the box will move relative to belt before coming to rest on it, taking g = 10 m s–2, is (a) 0.4 m (b) 1.2 m (c) 0.6 m (d) zero (Mains 2011) 39. A block of mass m is in contact with the cart C as shown in the figure. The coefficient of static friction between the block and the cart is m. The acceleration a of the cart that will prevent the block from falling satisfies (a) α μ > mg (b) α μ > g m (c) α μ ≥ g (d) α μ < g (2010) 40. A block B is pushed momentarily along a horizontal surface with an initial velocity V. If m is the coefficient of sliding friction between B and the surface, block B will come to rest after a time (a) gm/V (b) g/V (c) V/g (d) V/(gm) (2007) 41. The coefficient of static friction, ms, between block A of mass 2 kg and the table as shown in the figure is 0.2. What would be the maximum mass value of block B so that the two blocks do not move ? The string and the pulley are assumed to be smooth and massless. (g = 10 m/s2 ) (a) 2.0 kg (b) 4.0 kg (c) 0.2 kg (d) 0.4 kg (2004) 42. A block of mass 10 kg placed on rough horizontal surface having coefficient of friction m = 0.5, if a horizontal force of 100 N acting on it then acceleration of the block will be (a) 10 m/s2 (b) 5 m/s2 (c) 15 m/s2 (d) 0.5 m/s2 (2002) 43. On the horizontal surface of a truck a block of mass 1 kg is placed (m = 0.6) and truck is moving with acceleration 5 m/s2 then the frictional force on the block will be (a) 5 N (b) 6 N (c) 5.88 N (d) 8 N (2001) 44. A block has been placed on a inclined plane with the slope angle q, block slides down the plane at constant speed. The coefficient of kinetic friction is equal to (a) sinq (b) cosq (c) g (d) tanq (1993) 45. Consider a car moving along a straight horizontal road with a speed of 72 km/h. If the coefficient of static friction between the tyres and the road is 0.5, the shortest distance in which the car can be stopped is (taking g = 10 m/s2 ) (a) 30 m (b) 40 m (c) 72 m (d) 20 m (1992) 46. A heavy uniform chain lies on horizontal table top. If the coefficient of friction between the chain and the table surface is 0.25, then the maximum fraction of the length of the chain that can hang over one edge of the table is (a) 20% (b) 25% (c) 35% (d) 15% (1991) 47. Starting from rest, a body slides down a 45° inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between the body and the inclined plane is (a) 0.80 (b) 0.75 (c) 0.25 (d) 0.33 (1988) 5.10 Circular Motion 48. A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be (g = 10 m/s2 ) (a) 10 p rad/s (b) 10 rad/s (c) 10 2π rad/s (d) 10 rad/s (NEET 2019) 49. One end of string of length l is connected to a particle of mass m and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed v, the net force on the particle (directed towards centre) will be (T represents the tension in the string) (a) T mv l + 2 (b) T mv l − 2 (c) zero (d) T (NEET 2017) 50. A car is negotiating a curved road of radius R. The road is banked at an angle q. The coefficient of friction between the tyres of the car and the road is ms. The maximum safe velocity on this road is (a) g R s s μ θ μ θ + − tan 1 tan (b) g R s s 2 1 μ θ μ θ + − tan tan (c) gR s s 2 1 μ θ μ θ + − tan tan (d) gR s s μ θ μ θ + − tan 1 tan (NEET-I 2016) EduHulk.COM