Conservative and Non Conservative Forces

Q.

A particle free to move along the x-axis has potential energy given by $U\left(x\right)=k[1-exp(-x{)}^2]$ for $-\infty \le x\le +\infty$, where k is a positive constant of appropriate dimensions. Then

1. If its total mechanical energy is k/2, it has its minimum kinetic energy at the origin

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

3. For small displacements from x = 0, the motion is simple harmonic

4. At point away from the origin, the particle is in unstable equilibrium

Q.

Work done by a conservative force on a system is equal to

1. None of the above

2. The change in potential energy of the system

3. The change in kinetic energy of the system

4. The change in total mechanical energy of the system

Q.

A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to $\frac{-K}{r^2}$ , where K is a constant. The total energy of the particle is

1. 

2. 

3. 

4. 

Q. A non conservative force dissipates energy, while a conservative force does not dissipate energy

1. False
2. True

Q.

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 $W_1,W_{2}and{W}_3$ [IIT JEE 2003]

1. 

2. 

3. 

4. 

Q.

A body is moving up an inclined plane of angle $\theta$ with an initial kinetic energy E. The coefficient of friction between the plane and the body is $\mu$. The work done against friction before the body comes to rest is

1. $\frac{\mu cos\theta }{Ecos\theta +sin\theta }$

2. $\mu Ecos\theta$

3. $\frac{\mu Ecos\theta }{\mu cos\theta -sin\theta }$

4. $\frac{\mu Ecos\theta }{\mu cos\theta +sin\theta }$

Q. The work done by a force on a body, over a closed loop, is not always zero.

1. False
2. True

Q. During a round journey, work done by a conservative force is zero.

1. True
2. False

Q. When a non conservative force works on a system, total energy of the system remains constant.

1. False
2. True

Q. Friction is a conservative force.

1. False
2. True