8. An elevator without a ceiling is ascending with a constant speed of 6 m/s. A boy on the elevator throws a ball directly upward, from a height of 2.

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1 O. P. JINDAL SCHOOL, RAIGARH (CG) , INDIA Phone: , , (Extn , 02, 04, 06, 09); Fax: ; website: CLASS: XI- PHYSICS 1. A particle of mass m is projected in a resisting medium whose resistive force is F = kv and the initial velocity is v 0. (a) Find the expression for position and velocity in terms of time.(b) Find the time after which the velocity becomes v o /2. 2. A train travels from rest at one station to rest at another in the same straight line distant l.it moves over the first part of the distance with an acceleration of 1 m/s 2 and for the remainder with retardation of f2 m/s 2. Find time taken to complete the journey. 3. Three particles are located at the vertices of an equilateral triangle of side a. They all start moving simultaneously with a constant speed v but move in such a way that the first particle is continually headed for the second, the second for the third and the third for the first. Where and when will the particles converge? 4. A rubber ball is released from a height of 4.90 m above the floor. It bounces repeatedly, always rising to 81/100 of the height through which it falls. (a) Ignoring the practical fact that the ball has a finite size ( in other words, treating the ball as point mass that bounces an infinite number of times), show that its total distance of travel is 46.7 m. (b) Determine the time required for the infinite number of bounces. (c) Determine the average speed 5. In a car race, car A takes time t less to finish than car B and passes the finishing point with a velocity V more than car B. Assuming the cars starts from rest and travel with constant accelerations a 1 and a 2 respectively. Show that V 2 = a 1 a 2 t An elevator whose floor to the ceiling distance is 2.50 m, starts ascending with a constant acceleration of 1.25 m/s2.one second after the start, a bolt begins falling from the ceiling of the elevator. Calculate: (a) free fall time of the bolt.(b) thedisplacement and distance covered by the bolt during the free fall in the reference frame fixed to the shaft of the elevator. 7. A particle is projected vertically upwards from earth s surface with a velocity just sufficient to carry it to infinity. Find the time it takes in reaching a height h taking the radius of earth as R and the acceleration due to gravity at the surface as g.

2 8. An elevator without a ceiling is ascending with a constant speed of 6 m/s. A boy on the elevator throws a ball directly upward, from a height of 2.0 m above the elevator floor. At this time the elevator floor is 30 m above the ground. The initial speed of the ball with respect to the elevator is 9 m/s. (Take g = 10 m/s 2 ) (a) What maximum height above the ground does the ball reach? (b) How long does the ball take to return to the elevator floor? 9. The driver of a car moving at 30 m/s suddenly sees a truck that is moving in the same direction at 10 m/s and is 60 m ahead. The maximum deceleration of the car is 5 m/s2. (a) Will the collision occur if the driver s reaction time is zero? If so, when? (b) If the car driver s reaction time of 0.5 s is included, what is the minimum magnitude of deceleration required to avoid the collision? 10. A man who can swim with speed of 1 Km/h in still water wants to cross a river. He starts from a point A from the river bank and wants to reach the point B which is directly opposite to A. In what direction should he try to swim? Speed of the river flow is 0.5 Km/hr. Also find the time taken to cross the river if width is 10 m. 11. The system in the given figure remains at rest when the hanging weight w is 220 N. What are the magnitude and the direction of the frictional force on the 200 N block? 12. The block A in the given figure weighs 100 N. The coefficient of friction between the block and the surface on which it rests is The weight W is 20 N and the system is in equilibrium. Find the frictional force exerted on block A.

3 13. In the figure, the tension in the diagonal string is 60N (A) Find the magnitude of the horizontal forces F1 and F2 that must be applied to hold the system in the position shown(b) What is the weight of the suspended block. 14. A swimmer at point A on one side of river wants to reach at a point B on the other side by swimming only. Line AB makes angle 30 with the river flow. Velocity of swimmer is equal to velocity of river flow in magnitude. In what direction, with the line A should he try to swim to reach at B. 15. Block A of weight W slides down on inclined plane S of slope 37 at constant velocity while the plank B also weighing W rests on the top of A. The plank is attached by a cord to the top of the inclined plane. (a) Draw a diagram of all forces acting on A. (b) If the coefficient of kinetic friction is same between A and B and between S and A, determine its value.

4 16. Length of a uniform chain is L and coefficient of static friction is µ between the chain and the table top. Calculate the maximum length of the chain which can hang from the table without sliding. 17. An insect crawls on the inner surface of hemispherical bowl of radius r. If the coefficient of friction between an insect and bowl is µ and the radius of the bowl is r, find the maximum height to which the insect can crawl up. 18. A body of mass M is kept on a rough horizontal ground (static friction coefficient = µ). A person is trying to pull the body by applying a horizontal force F, but the body is not moving. What is the contact forcebetween the ground and the block. 19. Two blocks with masses m1=1 kg and m2 = 2 kg are connected by a string and slide down a plane inclined at an angle 45 with the horizontal. The coefficient of sliding friction between m1 and plane is µ 1 =0.4 and that between m2 and plane is µ 2 =0.2. Calculate the common acceleration of the two blocks and the tension in the string 20. A body of mass m rests on a horizontal floor with which it has a coefficient of static friction. It is desired to make the body move by applying the minimum possible force F. Find the magnitude of F and the direction in which it has to be applied. 21. A is a 100 kg block and B is a 200 kg block. As shown in fig., the block A is attached to a string tied to a wall. The coefficient of friction between A and B is 0.2 and the coefficient of friction between B and floor is 0.3. Then calculate the minimum force required to move the block B.(g =10 m/s 2 ).

5 22. In the given figure block A is placed on block B and both are placed on a smooth horizontal plane. Assume lower block to be sufficiently long. The force F pulling the block B horizontally is increased according to law F = 10t N (a) When does block A start slipping on block B? What will be force F and acceleration just before slipping starts? (b) When F is increased beyond the value obtained in part (a), what will be acceleration of A? (c) Draw acceleration-time graph. 23. Block A is placed on B and B is placed on block C, which rests on smooth horizontal ground as shown in the figure. Block A is pulled horizontally by a force F which increases gradually. (a) Decide sequence of slipping. (b) If F is increased gradually find acceleration of each block for all values of F. (c) If F = 15t N, draw a t graph. 24. Consider the figure shown here of a moving cart C. If the coefficient of friction between the block A and the cart is μ, then calculate the minimum acceleration a of the cart C so that the block A does not fall. 25. A hemispherical bowl of radius R is rotating about its axis of symmetry which is kept vertical. A small ball kept in the bowl rotates with the bowl without slipping on its surface. If the surface of the bowl is

6 smooth and the angle made by the radius through the ball with the vertical is β. Find the angular speed at which the bowl is rotating. 26. Find the magnitude of acceleration of centre of mass of the system. 27. Two smooth balls A and B, each of mass m and radius R, have their centre at (0, 0, R) and (5R, R, R) respectively, in a coordinate system as shown. Ball A, moving along positive x axis, collides with ball B. Just before the collision, speed of ball A is 4 m/s and ball B is stationary. The collision between the balls is elastic. Find the Velocity of the ball A just after the collision? 28. An artificial satellite (mass m) of a planet (mass M) revolves in a circular orbit whose radius is n times the radius R of the planet. In the process of motion, the satellite experiences a slight resistance due to cosmic dust. Assuming the force of resistance on satellite to depend on velocity as F=av 2 where 'a' is a constant, calculate how long the satellite will stay in the space before it falls onto the planet's surface. 29. If the law of gravitation be such that the force of attraction between two particles vary inversely as the 5/2 th power of their separation, then the graph of orbital velocity v 0 plotted against the distance r of a satellite from the earth's centre on a log-log scale is shown alongside. Find the slope of line.

7 30. Gravitational potential difference between a point on surface of planet and another point 10 m above is 4 J/kg. Considering gravitational field to be uniform, how much work is done in moving a mass of 2 kg from the surface to a point 5m above the surface? 31. A particle is projected vertically upwards the surface of the earth (radius R e ) with a speed equal to one fourth of escape velocity. What is the maximum height attained by it from the surface of the earth? 32. The escape velocity for a planet is v e. A particle starts from rest at a large distance from the planet, reaches the planet only under gravitational attraction, and passes through a smooth tunnel through its centre. Find its speed at the centre of the planet. 33. In a double star, two stars (one of mass m and the other of 2m) distant d apart rotate about their common centre of mass. Deduce an expression of the period of revolution. Show that the ratio of their angular momenta about the centre of mass is the same as the ratio of their kinetic energies. 34. A satellite moves eastwards very near the surface of the Earth in equatorial plane with speed (v 0 ). Another satellite moves at the same height with the same speed in the equatorial plane but westwards. If R = radius of the Earth and ωbe its angular speed of the Earth about its own axis. Then find the approximate difference in the two time period as observed on the Earth.