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**JEE Main Previous Year Papers Questions With Solutions Physics Work, Energy And Power**

**Multiple Choice with ONE correct answer**

**1.Two masses of 1 g and 4g are moving with equal kinetic energy. The ratio of the magnitudes of their momenta is [1980-2 marks]**

**Ans.**

**2.If a machine is lubricated with oil [1980-2 marks]**

**a)the mechanical advantage of the machine increases**

**b)the mechanical efficiency of the machine increases**

**c)both its mechanical advantage and efficiency increase**

**d)its effeciency increases, but its mechanical advantage decreases.**

**Ans.**(b) When a machine is lubricated with oil friction decreases. Hence the mechanical efficiency of the machine increases.

**3.A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration a**

_{c}is varying with time ‘t’ as a_{c}= k^{2}rt^{2 }where ‘k’ is a constant. The power delivered to the particle by the force acting on it is[1994-1 mark]**Ans.**

**4.A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest positon, and has a speed u. The magnitude of the change in its velocity as it reaches a positon where the string is horizontal is [1998-2 marks]**

**Ans.**

**5.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[1999-2 marks]**

**a) (2/3) k b) (3/2) k c) 3k d) 6k**

**Ans.**

**6.A wind-powered generator converts wind energy into electrical 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 [2000]**

**a) v b) v**

^{2}c) v^{3}d) v^{4}**Ans.**

**7.A particle, which is constrained to move along the 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 + ax**

^{3}. Here k and a are positive constants. For x>0, the functional graphically form of the potential energy U(x)of the particle is [2000]**Ans.**

**8.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 [2002]**

**Ans.**

**9.If W1, W**

_{2}and W_{3}respresent 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, W_{2}and W_{3 }[2003]**a)W1>W**

_{2}>W_{3}**b)W1 = W**

_{2}= W_{3}**c)W1 < W**

_{2}< W_{3}**d)W**

_{2}>W1 >W_{3}**Ans**.(b) The gravitational field is a conservative field.In a conservative field , the work done W does not depend on the path (from A to B). It depends on initial and final points W

_{1}=W

_{2}= W

_{3}

**10.A particle is acted by a force F=kx, where k is a +ve constant. Its potential energy at x=0 is zero. Which curve correctly represents the variation of potential energy of the block with respect to x ?[2004]**

**Ans.**

**Ans.**

**12.A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected to a time-dependent force F(t) in the x direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is**

**a) 4.50 J b) 7.50 J**

**c) 5.06 J d) 14.06 J**

**Ans.**

**Multiple Choice with ONE or More Than ONE correct answers**

**13.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 [1984-2 marks]**

**Ans.**

**14.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 to the table is [1985-2 marks]**

**a) MgL b) MgL/3**

**c) MgL/9 d) MgL/18**

**Ans.**

**15.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[1987-2 marks]**

**a)its velocity is constant**

**b)its acceleration is constant**

**c)its kinetic energy is constant**

**d)it moves in a circular path**

**Ans**.(c), (d) It is a case of uniform circular motion. Velocity and acceleration keep on changing th eir directions. Their magnitudes remain constant. Kinetic energy remains constant.Options (c) and (d) are correct.

**Ans.**

**17.A small ball starts moving from A over a fixed track as shown in the figure. Surface AB has friction. From A to B the ball rolls without slipping. Surface BC is frictionless. K**

_{A}, K_{B}and K_{c}are kinetic energies of the ball at A,B and C respectively. Then [2006-5 marks]**a)h**

_{A}> h_{c};K_{B}> K_{c b) hA > hc;KB > Kc}**c)h**

_{A}= h_{c};K_{B}= Kc d)h_{A}< h_{c};K_{B}> K_{c}**Ans.**

**Comprehension based questions**

**A small block of mass M moves on a frictionless surface of an inclined plane, as shown in the figure. The angle of the incline suddenly changes from 60° to 30° at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic (g=10 m/s**

^{2})**18.The speed of the block at point B immediately after it strikes the second incline is**

**Ans.**

**19.The speed of the block at point C, immediately before it leaves the second incline is**

**Ans.**

**20.If the collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is**

**Ans**.(c) The velocity of the block coming down from the incline AB makes an angle 30° with the incline BC. If the block collides with the incline BC elastically, the angle of velocity of the block after collision with the incline shall be 30°.Hence just after collision with the incline BC the velocity of block shall be horizontal. So immediately after the block strikes the second incline, its vertical component of velocity will be zero.

**Ans.**

**22.A pulley arrangement is shown in the figure. The cylinder A has a diameter of 30cm and the cylinder B has a diameter of 20cm. The working handle has an arm of 50cm. The direction of winding of the rope on A is opposite to that on B. Calculate the mechanical advantage of this arrangement. [1980]**

**Ans.**

**23.A body of mass 2kg is being dragged with a uniform velocity of 2m/s on a rough horizontal plane. The co-efficient of friction between the body and the surface is 0.20, J=4.2 joule/calorie and g = 9.8m/s**

^{2}. Calculate the amount of heat generated in 5 second. [1980-5 marks]**Ans.**

**24.In the figures (a) and (b), AC, DG and GF are fixed inclined planes, BC = EF = x and AB = DE = y. small block of mass is released from the point A. It slides down AC and reaches C with a speed v**

_{c}. The same block is released, from rest, from the point D. It slides down DGF and reaches the point F with speed v_{F}. The co-efficients of kinetic frictions, between the block and both the surfaces AC and DGF, are u Calculate v_{c}and v_{F}.[1980-6 marks]**Ans.**

**25.A lead bullet just melts when stopped by an obstacle. Assuming that 25 percent of the heat is absorbed by the obstacle, find the velocity of the bullet. Its initial temperature is 27°C .(Melting point of lead = 327° C, specific heat of lead = 0.03 calorie/g°C, latent heat of fusion of lead = 6 cal/g° C, J = 4.2 joule/calorie).[1981-3 marks]**

**Ans.**

**26.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 the 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 co-efficient of friction between the surfaces of blocks is 0.2. Force constant of the spring is 1960 newton/m. If mass of block A is 2kg, calculate the mass of block B and the energy stored in the spring. [1982-5 marks]**

**Ans**.Both A and B are moving with uniform speed. Their acceleration is zero and so the force on them should be zero. The spring is loaded. Let the extension of the spring be x. The force acting on the spring is the tension T. The tension T is set up in the string. Free body diagrams of B, spring and A are shown in the figures.

**27.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 newton/m. The part AB of the track is ffictionless 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/s**

^{2}).[1983-7 marks]**Ans.**The part AB of the track is frictionless. Hence no energy is lost along AB. The 0.5 kg block travels to spring and compresses the spring by an amount x. Energy is stored in the spring. Kinetic energy of block = Workdone against kinetic friction + potential energy of spring

**28.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? [1985-6 marks]**Ans.**

**29.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 small sphere A**

**Ans.**

**30.A block of mass 0.18 kg is attached to a spring of force-constant 2N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06m and comes to rest for the first time. The initial velocity of the block in m/s is V = N/10. Then N is [2011]**

**Ans.**

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