A force of 2i^+3j^+4k^N acts on a body for 4 second, produces a displacement of (3i^+4j^+5k^)m. The power used is-

(1) 9.5 W

(2) 7.5 W

(3) 6.5 W

(4) 4.5 W

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An engine pump is used to pump a liquid of density ρ continuously through a pipe of cross-sectional area A. If the speed of flow of the liquid in the pipe is v, then the rate at which kinetic energy is being imparted to the liquid is

(1) 12Aρv3

(2) 12Aρv2

(3) 12Aρv

(4) Aρv

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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

(1) MgL

(2) MgL/3

(3) MgL/9

(4) MgL/18

Concept Questions :-

Gravitational Potential energy
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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 

(1) W1 > W2 > W3

(2) W1 = W2 = W3

(3) W1 < W2 < W3

(4) W2 > W1 > W3

Concept Questions :-

Gravitational Potential energy
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A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to –K/r2, where K is a constant. The total energy of the particle is

1. K2r

2. K2r

3. Kr

4. Kr

Concept Questions :-

Potential energy: Relation with force
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The displacement x of a particle moving in one dimension under the action of a constant force is related to the time t by the equation t=x+3, where x is in meters and t is in seconds. The work done by the force in the first 6 seconds is 

(1) 9 J

(2) 6 J

(3) 0 J

(4) 3 J

Concept Questions :-

Concept of work
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A force F=K(yi+xj) (where K is a positive constant) acts on a particle moving in the xy-plane. Starting from 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 particles is 

(1) 2Ka2

(2) 2Ka2

(3) Ka2

(4) Ka2

Concept Questions :-

Work done by variable force
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If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of earth to a height equal to the radius of the earth R, is 

(1) 12mgR

(2) 2 mgR

(3) mgR

(4) 14mgR

Concept Questions :-

Gravitational Potential energy
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A lorry and a car moving with the same K.E. are brought to rest by applying the same retarding force, then 

(1) Lorry will come to rest in a shorter distance

(2) Car will come to rest in a shorter distance

(3) Both come to rest in a same distance

(4) None of the above

Concept Questions :-

Concept of work
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A particle free to move along the x-axis has potential energy given by U(x)=k[1e-x2] for x+, where k is a positive constant of appropriate dimensions. Then 

(1) At point away from the origin, the particle is in unstable equilibrium

(2) For any finite non-zero value of x, there is a force directed away from the origin

(3) If its total mechanical energy is k/2, it has its minimum kinetic energy at the origin

(4) For small displacements from x = 0, the motion is simple harmonic

Concept Questions :-

Potential energy: Relation with force
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