A particle of mass 0.1 *kg* is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at *x* = 0 , its velocity at *x* = 12 *m* is

(1) 0 *m/s*

(2) $20\sqrt{2}\text{\hspace{0.17em}}m/s$

(3) $20\sqrt{3}\text{\hspace{0.17em}}m/s$

(4) 40* m/s*

Concept Questions :-

Work done by variable force

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The relation between the displacement *X* of an object produced by the application of the variable force *F* is represented by a graph shown in the figure. If the object undergoes a displacement from *X* = 0.5 *m* to *X* = 2.5 *m* the work done will be approximately equal to

(1) 16 *J*

(2) 32 *J*

(3) 1.6 *J*

(4) 8 *J *

Concept Questions :-

Work done by variable force

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A particle is given a constant horizontal velocity from height h. Taking *g* to be constant every where, kinetic energy *E* of the particle *w. r. t.* time *t* is correctly shown in

(1)

(2)

(3)

(4)

Concept Questions :-

Concept of work

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The adjoining diagram shows the velocity versus time plot for a particle. The work done by the force on the particle is positive from

(1) *A* to *B*

(2) *B* to *C*

(3) *C* to *D*

(4) *D* to *E*

Concept Questions :-

Concept of work

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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 $F\left(x\right)=-kx+a{x}^{3}$. Here *k* and *a* are positive constants. For $x\ge 0$, the functional from of the potential energy *U*(*x*) of the particle is-

(1)

(2)

(3)

(4)

Concept Questions :-

Potential energy: Relation with force

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A force *F *acting on an object varies with distance *x *as shown here. The force is in *newton* and *x* in *metre*. The work done by the force in moving the object from *x* = 0 to *x* = 6 *m* is** **

(1) 4.5 *J*

(2) 13.5 *J*

(3) 9.0 *J*

(4) 18.0 *J*

Concept Questions :-

Work done by variable force

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The potential energy of a system is represented in the first figure. the force acting on the system will be represented by

(1)

(2)

(3)

(4)

Concept Questions :-

Potential energy: Relation with force

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A particle, initially at rest on a frictionless horizontal surface, is acted upon by a horizontal force which is constant in size and direction. A graph is plotted between the work done (*W*) on the particle, against the speed of the particle, (*v*). If there are no other horizontal forces acting on the particle the graph would look like

(1)

(2)

(3)

(4)

Concept Questions :-

Work-Energy theorem

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Which of the following graphs is correct between kinetic energy (*E*), potential energy (*U*) and height (*h*) from the ground of the particle

(1)

(2)

(3)

(4)

Concept Questions :-

Gravitational Potential energy

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The graph between $\sqrt{E}$ and $\frac{1}{p}$ is (*E *= kinetic energy and *p* = momentum)

1.

2.

3.

4.

Concept Questions :-

Concept of work

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Difficulty Level: