Title 5. Laws of Motion .pdf ✅

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