Tiêu đề 03B. WORK POWER ENERGY ( 71 - 85 ).pdf ✅

NISHITH Multimedia India (Pvt.) Ltd., 7 1 JEE MAINS - CW - VOL - I JEE ADVANCED - VOL - II NISHITH Multimedia India (Pvt.) Ltd., WORK POWER ENERGY LEVEL -VI SINGLE ANSWER QUESTIONS 1. An engine is pumping water continuously. The water passes through a nozzle with a velocity  . As water leaves the nozzle, the mass per unit length of the water jet is m0 . Find the rate at which kinetic energy is imparted to the water: A) 3 0 1 2 m v B) 2 0 1 2 m v C) 3 2 0 1 2 m v D) 1 2 0 1 2 m v 2. A hemispherical vessel of radius R moving with a constant velocity 0 v and containing a ball, is suddenly haulted. Find the height by which ball will rise in the vessel, provided the surface is smooth: A) 2 0 2 v g B) 2 0 2v g C) 2 0 v g D) none of these 3. Two balls of same mass are projected as shown, by compressing equally (say x) the springs of different force constants K1 and K2 by equal magnitude. The first ball is projected upwards along smooth wall and the other on the rough horizontal floor with coefficient of friction  . If the first ball goes up by height h , then the distance covered by the second ball will be: A) 2 1 2hK K B) 1 2 2 hK K C) 2 1 3 2 hK K D) 2 1 hK K 4. Two balls of masses m1 and m2 are placed on different platforms which are subjected to compression of same force constant and same compression. When platform is released, ball of mass m1 rises to maximum height in 4 seconds. Find the time in which other ball will rise to maximum height:(plat forms are mass less) A) 1 2 2m m B) 1 2 2 m m C) 2 1 1 2 m m D) 1 2 2 m m 5. A bob of mass m is suspended from a fixed support with a light string and the system with bob and support is moving with a uniform horizontal acceleration. The breaking strength of the string is mg 2 . Find the workdone by the tension in the string in the first one second: A) 2 2mg B) 2 2 mg C) 2 2 mg D) 2 mg 2 6. In the arrangement as shown M m  2 . Find the extension in the spring of force constant K1 . All pulleys are smooth and massless: A) 1   Mmg K M m B)   1 4 . Mmg K M m K  C) 1  2  Mmg K M m  D) 1   4 2 Mmg K M m  7. The total mechanical energy of a particle is E. The speed of the particle at 1 2 2E x K        is 1 2 2E m       . Find the potential energy of the particle at x : A) zero B) 1 2 2 Kx C) 1 2 4 Kx D) 2 2 5 Kx
7 2 NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL - II NISHITH Multimedia India (Pvt.) Ltd., WORK POWER ENERGY 8. The coefficient of friction between a particle moving with some velcoity V0 and the rough horizontal surface is 0 0 2 V gt      . Find how much kinetic energy is lost in time 0 t due to friction: A) 1/4 B) 1/2 C) 3/4 D) 2/3 9. N similar slab of cubical shape of edge b are lyging on ground. Density of material of slab is D. Work done to arrange them one over the other is : A) (N2 – 1) b3 Dg B) (N – 1) b4 Dg . C) 1/2 (N2 – N) b4 Dg D) (N2 – N) b4 Dg 10. A block A of mass m slides on a smooth slider in the system as shown. A block c of same mass hanging from a pulley pulls block A. When the block A was at position B, the spring was unstretched. Find the speed of the block A when AB OB L   A) 1 2 2 2 2 gL KL m        B)   1 2 2 2 2 1 2 KL gL m         C)   1 2 2 2 2 2 1 KL gL m         D) 1 2 2 2 2 gL KL m        11. A ring ‘A’ of mass ‘m’ is attached to a stretched spring of force constant K, which is fixed at C on a smooth vertical circular track of radius R. Points A and C are diametrically opposite. When the ring slips from rest on the track to point B, making an angle of 30 with AC. (   ACB 30 ) spring becomes unstretched. Find the velocity of the ring at B A)   1 2 2 2 2 3 3 2 KR gR m         B)   1 2 2 2 2 3 KR gR m         C)   1 2 2 2 2 2 3 3 KR gR m         D)   1 2 2 2 2 1 2 KR gR m         12. A and B are smooth light hinges equidistant from C, which can slide on ABC. The spring of force constant K is fixed at its one end C and connected to light rods AD and BD at point D. A block of mass m is suspended at D. Find the velocity of the block, when CAD changes from 30 to 45 . AD BD L   A)   1 2 2 2 2 1 2 KL gL m        

7 4 NISHITH Multimedia India (Pvt.) Ltd., JEE ADVANCED - VOL - II NISHITH Multimedia India (Pvt.) Ltd., WORK POWER ENERGY 18. 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. It slides down AC and reaches C with a speed VC . The small block is released from rest from the point D. It slides down DGF and reaches the point F with speed VF . The coefficients of kinetic frictions between the block and both the surfaces AC and DGF are m. Calculate VC and VF . A B C D E F G (a) (b) A) 1.7 m/s B) 2.7 m/s C) 3.7 m/s D) 0.7 m/s 19. A 0.5 kg block slides from the point A (see figure) on a horizontal track with an initial speed of 3m/s towards a weightless horizontal spring of length 1 m and force constant 2 Newton/m.The part AB of the track is frictionlessand 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 2m 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). A B D C A) 0.2 m B) 0.3 m C) 0.1 m D) 0.5 m MULTIPLE ANSWER QUESTIONS 20. The potential energy of a particle moving along x -axis is given by U x   20 5sin 4  , where U is in J and x is in metre under the action of conservative force: A) if total mechanical energy is 20 J, then at x = 7/8m, particle is at equilibrium B) if total mechanical energy is 20 J, then at x = 7/8m particle is not at equilibrium C) if total mechanical energy is 20 J, then at x = 3/8m, particle is at equilibrium D) if total mechanical energy is 20 J, then at x = 3/8m, particle is not at equilibrium 21. A block of mass 1 kg moves towards a spring of force constant 10 N/m. The spring is massless and unstretched. The coefficient of friction between block and surface is 0.30. After compressing the spring, block does not retun back: (g = 10 m/s) A) the maximum value of speed of block for which it is possible is 3.8 m/s B) the maximum value of speed of block for which it is possible is 4.2 m/s C) if Ei and Ef are initial and final mechanical energy, which is sum of kinetic energy and potential energy, then work done by friction on a system is (Ei - Ef ) D) statement in option (C) is wrong 22. The spring constant of spring A is twice the spring constant of spring B. Each of the spring is cut into two pieces. First piece of spring A is (4/5) of the total length. Second piece of spring B is (5/6) of its total length. Both springs are of equal length initially: . A) the ratio of force constant of first piece of spring B to the first piece of spring A is (12/5) B) the ratio of force constant of first piece of spring B to the first piece of spring A is 2 C) the ratio of force constant of second piece of spring A to the first piece of spring B is 5/3 D) the ratio of force constant of second piece of spring A to the first piece of spring B is 7/5 23. A particle of mass 1 kg is moving along X- axis. Its velocity is 6 m/s at x  0 . Acceleration-displacement curve and potential energy-displacement curve of the particle are shown: A) the work done by all the forces is 704 J B) the work done by external forces is 350 J C) the work done by external forces is 384 J D) the work done by conservation forces is 300J