MEDIUM
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Potential energy and displacement curve is given in diagram.

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The force at x=5 m is

 

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Important Questions on Work, Energy and Power

EASY
Two equal masses are attached to two each of a spring of spring constant k. The masses are pulled out symmetrically to stretch the spring by a length x over is natural length. The work done by the spring on each mass is
MEDIUM

The graphs below show the magnitude of the force on a particle as it moves along the positive X-axis from the origin to X=X1. The force is parallel to the X-axis and conservative. The maximum magnitude F1 has the same value for all graphs. Rank the situations according to the change in the potential energy associated with the force, least (or most negative) to greatest (or most positive).

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EASY

The figure shows the variation of potential energy with distance. The part of the graph which represents the repulsive force is

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MEDIUM

In the figure, mass of A is m and that of B is 2m. All the surface are smooth. System is released from rest with spring unstretched. Then, the maximum extension Xm in spring will be

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EASY
A block of mass 100 g moving at a speed of 2 m s-1 compresses a spring through a distance 2 cm before its speed is halved. Find the spring constant of the spring
MEDIUM

Two springs of force constants k1 and k2 are stretched by the same force. The ratio of potential energies stored in them is

EASY
A particle of mass m moves in a circular orbit under the central potential field, Ur=-Cr, where C is a positive constant. The correct radius - velocity graph of the particle's motion is :
HARD
Consider two masses with m1>m2 connected by a light inextensible string that passes over a pulley of radius R and moment of inertia I about its axis of rotation. The string does not slip on the pulley and the pulley turns without friction. The two masses are released from rest separated by a vertical distance 2h. When the two masses pass each other, the speed of the masses is proportional to
EASY
If a spring of spring constant 200 N m-1 is compressed by 5 cm, then the energy stored in the spring is
MEDIUM
The potential energy function for a two dimensional force is given by U=3x3y-7x. The force that acts at the point x, y is (Take i^ and j^ as unit vectors along X- and Y- axes)
EASY
Potential energy as a function of r is given by U=Ar10-Br5, where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :
MEDIUM
A particle with total mechanical energy which is small and negative is under the influence of a one dimensional potential Ux=x44-x22 J, where x is in meters. At time t=0 s, it is at x=-0.5 m. Then at a later time it can be found,
MEDIUM
A 0.5 kg block moving at a speed of 12 m s-1 compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be _____ N m-1.
HARD

Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that Emech =8 J, the incorrect statement for this system is :

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EASY
The potential energy of a system increases if work is done
MEDIUM
A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g=9.8 ms-2 :
EASY
Two particles A and B of same mass have their de-Broglie wavelengths in the ratio XA :XB=K :1. Their potential energies UA :UB=1 :K2. The ratio of their total energies EA :EB is
MEDIUM
A particle is released from a height H. At a certain height its kinetic energy is half of its potential energy with reference to the surface of the earth. Height and speed of the particle at that instant are respectively
MEDIUM
A uniform chain of mass  M and length L is lying on a smooth horizontal table, with half of its length hanging down. The work done in pulling the entire chain up the table is
HARD
A particle is moving in a circle of radius r under the action of a force F=αr2 which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy=0 for r=0):