Conservative and Non Conservative Forces

Q.

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

1. The change in total mechanical energy of the system

2. The change in kinetic energy of the system

3. The change in potential energy of the system

4. None of the above

Q. Potential energy is defined } a. Only in conservative field } b.As the negative of work done by conservative } forces } c.As the negative of workdone by external } forces when }Δ K=0 dAll of these

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. The potential energy function for a conservative forceis given by U = B(2x + 4y). The work done by theconservative force in displacing a particle from pointP(1, 2) to Q(3, 5) is equal to(2) 26B(1) 10B10 B(4)+(3) 16 Bstraight line on a frictionlessthen

Q.

Consider two masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their speeds are such that they complete circular motion in the same time t. The ratio of their untripetal acceleration is,

1. m₁r₁:m₂r₂

2. m₁:m₂

3. r₁:r₂

4. 1:1

Q. Answer the following : (a) The casing of a rocket in flight burns up due to friction. At whose expense is the heat energy required for burningobtained? The rocket or the atmosphere? (b) Comets move around the sun in highly elliptical orbits. The gravitational force on the comet due to the sun is not normal to the comet’s velocity in general. Yet the work done by the gravitational force over every complete orbit of the comet is zero. Why ? (c) An artificial satellite orbiting the earth in very thin atmosphere loses its energy gradually due to dissipation against atmospheric resistance, however small. Why then does its speed increase progressively as it comes closer and closer to the earth ? (d) In Fig. 6.13(i) the man walks 2 m carrying a mass of 15 kg on his hands. In Fig. 6.13(ii), he walks the same distance pulling the rope behind him. The rope goes over a pulley, and a mass of 15 kg hangs at its other end. In which case is the work done greater ?

Q. Let $V_G$ and $E_G$ denote the gravitational potential and field respectively in a region, then choose the wrong statement.

1. $V_G\ne 0,E_G=0$
2. $V_G\ne 0,E_G\ne 0$
3. $V_G=0,E_G\ne 0$
4. $V_G=0,E_G=0$

Q. If $U_1,U_2$ represents "change in potential energy" of a body with mass $m$ moving from $A$ to $B$ along two different paths $1$, & $2$ (as shown in the figure) in the gravitational field. Then

1. $U_1=U_2$
2. $U_1>U_2$
3. $U_1<U_2$
4. $U_1\ge U_2$

Q. A particle moves along a curve of unknown shape but magnitude of force $\overrightarrow{F}$ is constant and always acts along the tangent to the curve. Then,

1. $\overrightarrow{F}$ must be conservative
2. $\overrightarrow{F}$ may be conservative
3. $\overrightarrow{F}$ must be non-conservative
4. $\overrightarrow{F}$ may be non-conservative

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

1. False
2. True

Q. Is work done by a spring is applying conservative force?

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 $W_1,W_{2}and{W}_3$

1. 

2. 

3. 

4. 

Q. A spring is initially compressed by $2\text{m}$. Find out the work done required to compress another $6\text{m}$ if spring constant $k=2\text{N/m}$.

1. $60\text{J}$
2. $32\text{J}$
3. $68\text{J}$
4. $36\text{J}$

Q. The potential energy of a conservative system is given by $U=A{x}^2-Bx$, where $x$ represents the position of the particle. $A$ and $B$ are positive constants. Then

1. Force acting on the system will be $(B-2Ax)$
2. At equilibrium, potential energy will be $\frac{-B^2}{4A}$
3. system is in stable equilibrium.
4. None

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. 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

Q.

Work done in motion of the body over a closed loop for conservative forces is

1. infintesimal

2. infinity

3. non-zero

4. zero

Q. Which of the following force is conservative force?

1. $\overrightarrow{F}=-3y\hat{i}-4x\hat{j}$
2. $\overrightarrow{F}=5y\hat{i}-5x\hat{j}$
3. $\overrightarrow{F}=3y\hat{i}+4x\hat{j}$
4. $\overrightarrow{F}=-5y\hat{i}-5x\hat{j}$

Q. If the energy stored in spring '$\text{A}$' is $20\text{J}$, then energy stored in spring '$\text{B}$' is (under the same stretching force)

1. $10\text{J}$
2. $25\text{J}$
3. $40\text{J}$
4. $35\text{J}$

Q. In the Column I below, four different paths of a particle are given as functions of time.
In these functions, $\alpha$ and $\beta$ are positive constants of appropriate dimensions and $\alpha \ne \beta .$ In each case, the force acting on the particle is either zero or conservative.
In Column II, five physical quantities of the particle are mentioned: $\overrightarrow{p}$ is the linear momentum $\overrightarrow{L}$ is the angular momentum about the origin, $K$ is the kinetic energy, $U$ is the potential energy and $E$ is the total energy.
Match each path in Column I with those quantitites in Column II, which are conserved for that path.
$\begin{array}{cc}\text{Column~I}& \text{Column~II}\\ \left(A\right)\overrightarrow{r}\left(t\right)=\alpha t\hat{i}+\beta t\hat{j}& 1.\overrightarrow{p}\\ \left(B\right)\overrightarrow{r}\left(t\right)=\alpha \cos \omega t\hat{i}+\beta \sin \omega t\hat{j}& 2.\overrightarrow{L}\\ \left(C\right)\overrightarrow{r}\left(t\right)=\alpha (\cos \omega \hat{i}+\sin \omega t\hat{j})& 3.K\\ \left(D\right)\overrightarrow{r}\left(t\right)=\alpha t\hat{i}+\frac{\beta }{2}{t}^2\hat{j}& 4.U\\ & 5.E\end{array}$

1. $A\to 1,2,3,4,5;B\to 2,5;C\to 2,3,4,5;D\to 5$
2. $A\to 1,2,3,4,5;B\to 3,5;C\to 1,2,3,4;D\to 4$
3. $A\to 1,2,3,4,5;B\to 1,5;C\to 2,3,4,5;D\to 1$
4. $A\to 1,2,3,4,5;B\to 4;C\to 1,3,4,5;D\to 3$

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. 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

Q. A ball of mass $400\text{g}$ is dropped to the ground from a height of $30\text{m}$. The ball bounces back multiple times before coming to rest. Which of the following statements is correct?

1. The work done by air resistance increases if the ball bounces more number of times.
2. The kinetic energy of the ball increases if the ball bounces more number of times.
3. The work done by gravity increases if the ball bounces more number of times.
4. The potential energy of the ball increases as the ball bounces.

Q. A particle, which is constrained to move along the $x-$ axis, is subjected to a force from the origin as $F\left(x\right)=-kx+a{x}^3$. Here $k$ and $a$ are positive constants. For $x=0$, the functional form of the potential energy $U\left(x\right)$ of particle is

1. 
2. 
3. 
4. 

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

1. True
2. False

Q. The potential energy $U$ of a particle of mass $m=1\text{kg}$ moving in $x-y$ plane is given by $U=3x+4y,$ where $x$ and $y$ are in metre and $U$ is in joule. If initially particle was at rest, then its speed at $t=2\text{s}$ will be

1. $10\text{m/s}$
2. $6\text{m/s}$
3. $8\text{m/s}$
4. $7\text{m/s}$

Q.

Which of the following statement is not related to conservative force?

1. Work done is recoverable

2. Path dependent

3. Work done in closed path is zero

4. Path independent

Q. The potential energy (in SI units) of a particle of mass $2\text{kg}$ in a conservative field is $U=6x-8y$. If the initial velocity of the particle is $\overrightarrow{u}=-1.5\hat{i}+2\hat{j}\text{m/s},$ then the total distance travelled by the particle in first two seconds is

1. $10\text{m}$
2. $12\text{m}$
3. $15\text{m}$
4. $18\text{m}$

Q. Potential energy is defined Options: Should have chosen Only in conservative fields As the negative of work done by conservative forces As the negative of workdone by external forces when ΔK = 0

Q. 108.what is relation bw work done by conservative and nonconservative force

Q. In the Column I below, four different paths of a particle are given as functions of time.
In these functions, $\alpha$ and $\beta$ are positive constants of appropriate dimensions and $\alpha \ne \beta .$ In each case, the force acting on the particle is either zero or conservative.
In Column II, five physical quantities of the particle are mentioned: $\overrightarrow{p}$ is the linear momentum $\overrightarrow{L}$ is the angular momentum about the origin, $K$ is the kinetic energy, $U$ is the potential energy and $E$ is the total energy.
Match each path in Column I with those quantitites in Column II, which are conserved for that path.
$\begin{array}{cc}\text{Column~I}& \text{Column~II}\\ \left(A\right)\overrightarrow{r}\left(t\right)=\alpha t\hat{i}+\beta t\hat{j}& 1.\overrightarrow{p}\\ \left(B\right)\overrightarrow{r}\left(t\right)=\alpha \cos \omega t\hat{i}+\beta \sin \omega t\hat{j}& 2.\overrightarrow{L}\\ \left(C\right)\overrightarrow{r}\left(t\right)=\alpha (\cos \omega \hat{i}+\sin \omega t\hat{j})& 3.K\\ \left(D\right)\overrightarrow{r}\left(t\right)=\alpha t\hat{i}+\frac{\beta }{2}{t}^2\hat{j}& 4.U\\ & 5.E\end{array}$

1. $A\to 1,2,3,4,5;B\to 2,5;C\to 2,3,4,5;D\to 5$
2. $A\to 1,2,3,4,5;B\to 3,5;C\to 1,2,3,4;D\to 4$
3. $A\to 1,2,3,4,5;B\to 1,5;C\to 2,3,4,5;D\to 1$
4. $A\to 1,2,3,4,5;B\to 4;C\to 1,3,4,5;D\to 3$

Q. is change in potential energy is equal to negative of work done?