A force of $2\hat{i}+3\hat{j}+4\hat{k}\text{\hspace{0.17em}}N$ acts on a body for 4 second, produces a displacement of $(3\hat{i}+4\hat{j}+5\hat{k})m.$ The power used is-

(1) 9.5 *W*

(2) 7.5 *W *

(3) 6.5 *W*

(4) 4.5 *W *

Concept Questions :-

Power

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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) $\frac{1}{2}A\rho {v}^{3}$

(2) $\frac{1}{2}A\rho {v}^{2}$

(3) $\frac{1}{2}A\rho v$

(4) $A\rho v$

Concept Questions :-

Power

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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 *W*_{1}, *W*_{2} and *W*_{3} 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 *W*_{1}, *W*_{2} and *W*_{3}** **

(1) *W*_{1} > *W*_{2} > *W*_{3}

(2) *W*_{1} = *W*_{2} = *W*_{3}

(3) *W*_{1} < *W*_{2} < *W*_{3}

(4) *W*_{2} > *W*_{1} > *W*_{3}

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*/*r*^{2}, where *K* is a constant. The total energy of the particle is

1. $\frac{K}{2r}$

2. $-\frac{K}{2r}$

3. $-\frac{K}{r}$

4. $\frac{K}{r}$

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 $t=\sqrt{x}+3$, 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 $\mathit{F}=-K(y\mathit{i}+x\mathit{j})$ (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) $-2K{a}^{2}$

(2) $2K{a}^{2}$

(3) $-K{a}^{2}$

(4) $K{a}^{2}$

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) $\frac{1}{2}mgR$

(2) 2 *mgR *

(3) *mgR *

(4) $\frac{1}{4}mgR$

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 $U\left(x\right)=k[1-{e}^{-{x}^{2}}]$ for $-\infty \le x\le +\infty $, 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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