LOM-05-SUBJECTIVE SOL.C.B.S.E. LEVEL - I

LEVEL - I (C.B.S.E.) (REVIEW YOUR CONCEPTS ) 1. A man of mass 70 kg stands on weighting scale in a lift which is moving (a) upwards with a uniform speed of 10 ms-1. (b) downwards with a uniform acceleration of 5 ms-2. (c) upwards with a uniform acceleration of 5 ms-2. What would be the readings on the scale in each case? (d) What would be the reading if the lift mechanism failed and it hurtled down freely under gravity? 2. Figure shows the position-time graph of a particle of mass 4 kg. What is the force on the particle for t  0, t  4 s, 0  t  4s ? (Consider one-dimensional motion only). 3. Two billiard balls each of mass 0.05 kg moving in opposite directions with speed 6 ms-1 collide and rebound with the same speed. What is the change in momentum of each ball due to the other? 4. Figure shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with 1 ms-2. What is the net force on the man? If the coefficient of static friction between the man’s shoes and the belt is 0.2, up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Mass of the man = 65 kg). 5. A block of mass 25 kg is raised by a 50 kg man in two different ways as shown in Figure. What is the action on the floor by the man in the two cases? If the floor yields to a normal force of 700 N, which mode should the man adopt to lift the block without the floor yielding? 6. A monkey of mass 40 kg climbs on a rope which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey (a) climbs up with an acceleration of 6 ms-2. (b) climbs down with an acceleration of 4 ms-2. (c) climbs up with a uniform speed of 5 ms-1. (d) falls down the rope nearly freely under gravity? 7. The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown in figure. The co-efficient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with 2 ms-2. At what distance from the starting point does the box fall off the truck? (Ignore the size of the box). 8. A thin circular wire of radius R rotates about its vertical diameter with an angular frequency  . Show that a small bead on the wire remains at its lowermost point for   g / R . What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for   ? Neglect friction. 9. A helicopter of mass 1000 kg rises with a vertical acceleration of 15 m s -2. The crew and the passengers weigh 300 kg. Give the magnitude and direction of the (a) force on the floor by the crew and passengers. (b) action of the rotor of the helicopter on the surrounding air. (c) force on the helicopter due to the surrounding air. 10. A block of mass 15 kg is placed on a long trolley. The co-efficient of static friction between the block and the troley is 0.18. The trolley accelerates from rest with 0.5 m s-2 for 20 s and then moves with uniform velocity. Discuss the motion of the block as viewed by (a) a stationary observer on the ground. (b) an observer moving with the trolley. 11. Both the springs shown in figure are unstretched. If the block is displaced by a distance x and released, what will be the intial acceleration? 12. Three equal weights of 2 kg each are hanging over a frictionless pulley.Find the acceleration of the system and tension of the string connecting weights A and B [g =9.8 m/s2] 13. A cyclist goes around a horizontal curve of radius r with a speed v. Find the angle  with the vertical made by the cyclist while going around the curve. O 14. Find the tension in OB and AB in the given figure. Also, calculate the tension in OB when just after the string AB is burnt. A 15. A block placed on smooth horizontal surface is split into two blocks of masses m and m2 along a smooth incliened plane making an angle α 1 with the horozontal. Find the ratio of their horizontal accelerations.