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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The kinetic energy acquired by a mass m in travelling a certain distance d starting from rest under the action of a constant force is directly proportional to 

(1) m

(2) Independent of m

(3) 1/m

(4) m

Concept Questions :-

Concept of work
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An open knife edge of mass 'm' is dropped from a height 'h' on a wooden floor. If the blade penetrates upto the depth 'd' into the wood, the average resistance offered by the wood to the knife edge is 

(1) mg

(2) mg1hd

(3) mg1+hd

(4) mg1+hd2

Concept Questions :-

Gravitational Potential energy
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A body is moving along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to 

(1) t1/2

(2) t3/4

(3) t3/2

(4) t2

Concept Questions :-

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A batsman hits a sixer and the ball touches the ground outside the cricket field. Which of the following graph describes the variation of the cricket ball's vertical velocity v with time between the time t1 as it hits the bat and time t2 when it touches the ground 

(1)

(2)

(3)

(4)

Concept Questions :-

Work-Energy theorem
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The relationship between force and position is shown in the figure given (in one dimensional case). The work done by the force in displacing a body from x = 1 cm to x = 5 cm is -

(1) 20 ergs

(2) 60 ergs

(3) 70 ergs

(4) 700 ergs

Concept Questions :-

Work done by variable force
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The pointer reading v/s load graph for a spring balance is as given in the figure. The spring constant is-

(1) 0.1 N/cm

(2) 5 N/cm

(3) 0.3 N/cm

(4) 1 N/cm

Concept Questions :-

Elastic potential energy
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