1. IIT JEE -Physics Work, Power, and Energy

2. SECTION – I OBJECTIVE QUESTIONS Only one option is correct

3. 01 Problem 1980 Two masses of 1 g and 4 g are moving with equal kinetic energies. The ratio of the magnitude of their momenta is : 4 : 1 √2: 1 1 : 2 1 : 16

4. 02 Problem 1984 A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to : t1/2 t3/4 t3/2 t2

5. 03 Problem 1985 A uniform chain of length L and mass M is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on the table is : MgL MgL/3 MgL/9 MgL/18

6. 04 Problem 1994 A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac is varying with time t as ac = k2 rt2, where k is a constant the power delivered to the particle by the force acting on it is: 2πmk2r2 mk2r2t (mk4r2t5)/3 zero

7. 05 Problem 1998 A stone tied to a sting or length L is whirled in a vertical circle with the other end of the string at the center. At a certain instant of time, the stone is at its lower position, and has a speed u. the magnitude of the change in its velocity as it reaches a position where the string is horizontal is :

8. 06 Problem 1998 A force (where K is a positive constant) acts on a particle moving in the x-y plane. Starting form the origin, The particle is taken along the positive x-axis to the point (a,0) and then parallel to the y-axis to the point (a,a). The total work done by the force F on the particle is : -2 Ka2 2 Ka2 - Ka2 Ka2

9. 07 Problem 1999 A spring of force- constant K is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force-constant of : (2/3)k (3/2)k 3 k 6 k

10. 08 Problem 2001 A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to : v v2 v3 v4

11. 09 Problem 2002 A particle, which is constrained to move along x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F(x) = - kx + ax3. Here, k and a are positive constant. For x 0, the functional form of the potential energy U(x) of the particle is :

12. 10 Problem 2002 An ideal spring with spring-constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is:

13. 11 Problem 2002 A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector a is correctly shown in :

14. 12 Problem 2003 If W1, W2 and W3 represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass m. find the correct relation between W1, W2 and W3 : W1 > W2 > W3 W1 = W2 = W3 W1 < W2 < W3 W2 > W1 > W3

15. 13 Problem 2004 A particle is placed at the origin and a force F = kx is acting on it (where k is a positive constant). If U (0) = 0, the graph of U (x) versus x will be (where U is the potential energy function) :

16. SECTION – II OBJECTIVE QUESTIONS More than one options are correct

17. 01 Problem 1987 A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that: Its velocity is constant Its acceleration is constant Its acceleration is constant It moves in a circular path

18. SECTION – III SUBJECTIVE QUESTIONS

19. 01 Problem 1980 In the figures (a) and (b) AC, DG and GF are fixed inclined planes, BC = EF = x and AB = DE = y. A small block of mass M is released from the point A. Its slides down AC and reaches C with a speed Vc. The same block is released from rest from the point D. Its slides down DGF and reaches the point F with speed VF. The coefficients Of kinetic frictions between block and both the surfaces AC and DGF are . Calculate VC and VF.

20. 02 Problem 1980 A body of mass 2 kg is being dragged with a uniform velocity of 2 m/s on a rough horizontal plane. The coefficient of friction between the body and the surface is 0.20, J = 4.2 J/cal and g =9.8 m/s2. Calculate the amount of heat generated in 5 sec.

21. 03 Problem 1981 A led bullet just melts when stopped by an obstacle Assuming that 25 per cent of the heat is absorbed by the obstacle, find the velocity of the bullet if its initial temperature is 270C. (Melting point of lead = 3270 C, specific heat of lead = 0.03 cal/g-C0, latent heat of fusion of lead = 6 cal/g-0C, J = 4.2 Joule/calorie).

22. 04 Problem 1993 Two blocks A and B are connected to each other by a string and a spring; the string passes over a frictionless pulley as shown in figure. Block B slides over the horizontal top surface of a stationary block C and the block A slides along the vertical side of C, both with the same uniform speed. The coefficient of friction between the surfaces of blocks is 0.2. Force constant of the spring is 1960 N/m. If mass of block A is 2 kg. Calculate the mass of block B and the energy stored in the spring.

23. 05 Problem 1983 A 0.5 kg block slides from the point A (see fig.) on a horizontal track with an initial speed of 3 m/s towards a weightless horizontal spring of length 1 m and force constant 2 N/m. the part AB of the track is frictionless and the part BC has the coefficients of static and kinetic friction as 0.22 and 0.2 respectively. If the distances AB and BD are 2 m and 2.14 m respectively, find the total distance through which the block moves before it comes to rest completely.(Take g =10 m/s2).

24. 06 Problem 1985 A string, with one end fixed on a rigid wall, passing over a fixed frictionless pulley at a distance of 2 m from the wall, has a point mass M = 2 kg attached to it at a distance of 1 m from the wall. A mass m = 0.5 kg attached at the free end is held at rest so that the string is horizontal between the wall and the pulley and vertical beyond the pulley. What will be the speed with which the mass M will hit the wall when the mass m is released?

25. 07 Problem 1988 A bullet of mass M is fired with a velocity 50 m/s at an angle θ with the horizontal. At the highest point of its trajectory, it collides head-on with a bob of mass 3 M suspended by a massless string of length 10/3 metres and gets embedded in the bob. After the collision the string move through an angle of 1200. Find : The angle θ, The vertical and horizontal co-ordinates of the initial position of the bob with respect to the point of firing of the bullet. (Take g = 10 m/s2)

26. 08 Problem 1999 A particle is suspended vertically from a point O by an inextensible massless string of length L. A vertical line AB is at a distance L/8 from O as shown in figure. The object is given a horizontal velocity u. At some point, its motion ceases to be circular and eventually the object passes through the line AB. At the instant of crossing AB< its velocity is horizontal. Find u.

27. 09 Problem 2004 A spherical ball of mass m is kept at the highest point in the space between two fixed, concentric spheres A and B (see figure). The smaller sphere A has a radius R and the space between the two spheres has a width d. The ball has a diameter very slightly less then d. All surfaces are frictionless. The ball is given a gentle push(towards the right in the figure). The angle made by the radius vector of the ball with the upward vertical is denoted by θ. Express the total normal reaction force exerted by the spheres on the ball as a function of a angle θ. Let NA and NB denote the magnitudes of the normal reaction forces on the ball exerted by the spheres A and B, respectively. Sketch the variations of NA and NB as function of cos θ in the range 0≤θ≤πby drawing two separate graphs in your answer book, taking cosθ on the horizontal axis.

28. 10 Problem 2005 Two identical ladders are arranged as shown in the figure. Mass of each ladder is M and length L. The system is in equilibrium. Find direction and magnitude of frictional force acting at A or B.

29. 11 Problem 2006 A circular disc with a groove along its diameter is placed horizontally. A block of mass 1 kg is placed as shown. The coefficient of friction between the block and all surfaces of groove in contact is μ=2/5. The disc has an acceleration of 25 m/s2. Find the acceleration of the block with respect of disc.