Work Energy And Power

If a machine is lubricated with oil

A box is moved along a straight line by a machine delivering constant power. The distance moved by the body in time is proportional to

A uniform chain of length and mass is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If is acceleration due to gravity, work required to pull the hanging part on to the table is

A particle of mass is moving in a circular path of constant radius such that centripetal acceleration varying with time is where is a constant. What is the power delivered to the particle by the force acting on it?

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

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

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

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) . Here, k and a are positive constants. For , the functional form of the potential energy U (x) of the particle is

If and 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

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)

A block (5) is attached to two unstretched springs with spring constants k and 4k, respectively. The other ends are attached to two supports and not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio is

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 s is

A particle of mass is projected from the ground with an initial speed at an angle with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed . The angle that the composite system makes with the horizontal immediately after the collision is

A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from to , the force it applies on the wire is

A particle of mass is initially at rest at the origin. It is subjected to a force and starts moving along the -axis. Its kinetic energy changes with time as , where is a positive constant of appropriate dimensions. Which of the following statements is (are) true?