Relation between Work Done and PE

Q. The potential energy of a system increases if work is done

1. upon the system by a non conservative force.
2. on the system against a conservative force.
3. by the system against a non conservative force.
4. upon the system by a conservative force.

Q.

A force acts on a 30 gm particle in such a way that the position of the particle as a function of time is given by $x=3t-4t^2+t^3$, where x is in metres and t is in seconds. The work done during the first 4 seconds is

1. 5.28 J

2. 450 mJ

3. 490 mJ

4. 530 mJ

Q.

The potential energy of a system increases if work is done

1. on the system against a conservative force.
2. upon the system by a non-conservative force.
3. by the system against a conservative force.
4. upon the system by a conservative force.

Q.

A body of mass m rises to height $h=\frac{R}{5}$ from the earths surface, where R is earths radius. If g is acceleration due to gravity at earths surface, the increase in potential energy is

1. 

2. 

3. 

4. mgh

Q. The energy E of an oscillating body in simple harmonic motion depends on its mass M , freguency N and amplitude A . using the method of dimension analysis find the relation between E , M, N , and A

Q.

Work done by Conservative force is Positive,

Can I say Kinetic Energy increases?

Q. A steel rod of length 1 m is heated from ${25}^{\circ }C$ to ${75}^{\circ }C$ keeping its length constant. The longitudinal strain developed in the rod is (Given: Coefficient of linear expansion of steel $=12\times {10}^{-6}{/}^{\circ }C)n\times {10}^{-4}$ . Report n.

Q.

When work is done on a body by an external force, its

1. Only potential energy increases

2. Only kinetic energy increases

3. Both kinetic and potential energies may increase

4. Sum of kinetic and potential energies remains constant

Q.

Consider the situation shown in figure. All the surfaces are frictionless and the string and the pulley are light. Find the magnitude of the acceleration of the two blocks.

Q. A mass of 1 kg is acted upon by a single force $\overrightarrow{F}=(4\hat{i}+4\hat{j})N.$
Under this force it is displaced from (0, 0 ) to (1 m, 1 m). If initially the speed of the particle was 2 m/s, its final speed should be

1. 6 m/s
2. 4.5 m/s
3. 8 m/s
4. 4 m/s

Q.

The two blocks in an Atwood machine have masses 2.0 kg and 3.0 kg. Find the work done by gravity during the fourth second after the system is released from rest.

Q.

A block of mass 2 kg is placed on a horizontal surface having kinetic friction 0.4 and static friction 0.5. If the force applied on the body is 2.5 N, then the frictional force acting on the body will be.

1. 8 N.

2. 10 N.

3. 20 N.

4. 2.5 N.

Q. For a particle executing SHM, the displacement $x$ is given by $x=A\cos \omega t$. Choose the graph which represents the variation of potential energy as a function of time $t$ and displacement $x$.

1. $I,III$
2. $I,IV$
3. $II,III$
4. $II,IV$

Q.

A force that does not depend on the path taken to increase the potential energy is __________.

Q. Work done by a conservative force is equal to negative change in the potential energy of the system.

1. False
2. True

Q. Consider a rain drop of mass $1\text{g}$ falling from a height of $2\text{km}$. It hits the ground with a speed of $50\text{m/s}$. The work done by resistive force of air is
$(g=10{\text{m/s}}^2)$

1. $-187.5\text{J}$
2. $43.75\text{J}$
3. $-18.75\text{J}$
4. $14.375\text{J}$

Q. A man places a chain (of mass ${}^{\prime }{m}^{\prime }$ and length ${}^{\prime }{L}^{\prime }$) on a table slowly. Initially the lower end of the chain just touches the table. The man drops the chain when half of the chain is in vertical position. Then work done by the man in this process is:

1. $-mg\frac{L}{2}$
2. $-\frac{mgL}{4}$
3. $-\frac{3mgL}{8}$
4. $-\frac{mgL}{8}$

Q. A uniform chain of mass $m$ and length $L$ hangs on a table with two thirds of its length on the table. The work done by a person to put the hanging part back on the table will be

1. $\frac{mgL}{9}$
2. $\frac{mgL}{18}$
3. $\frac{mgL}{27}$
4. $mgL$

Q.

A solid sphere of mass 0.50 kg is kept on a horizontal surface. The coefficient of static friction between the surfaces in contact is $\frac{2}{7}$. What maximum force can be applied at the highest point in the horizontal direction so that the sphere does not slip on the surface ?

Q.

Three blocks A, B and C are kept as shown in the figure. The coefficient of friction between A and B is 0.2, B and C is 0.1, C and between C and ground is 0.0. The masses of A, B and C are 3 kg, 2kg and 1 kg respectively, A is given a horizontal velocity 2 m/s. A, B and C always remain in contact. Find (in J) the magnitude of total work done by friction.

$K_f-K_i=W_{friction}$ (K= Kinetic energy)

1. 6 J

2. 3 J

3. -6 J

4. -3 J

Q. There are two massless springs A and B of spring constant $K_A$ and $K_B$ respectively and $K_A>K_B$. If $W_A$ and $W_B$ be denoted as work done on A and work done on B respectively, then

1. If they are compressed to same distance, $W_A>W_B$
2. If they are compressed by same force (upto equilibrium state) $W_A<W_B$
3. If they are compressed by same distance, $W_A<W_B$
4. If they are compressed by same force (upto equilibrium state) $W_A>W_B$

Q.

Potential energy and kinetic energy together form mechanical energy.

1. True
2. False

Q. The potential energy of a conservative system is given by
$U=a{x}^2-bx$
Here $a$ and $b$ are positive constants. Then, choose the correct option.

1. The equilibrium position is $x_{eq}=\frac{b}{2a}$ and it is a point of stable equilibrium.
2. The equilibrium position is $x_{eq}=\frac{b}{2a}$ and it is a point of unstable equilibrium.
3. The equilibrium position is $x_{eq}=\frac{b}{2a}$ and it is neutral equilibrium.
4. The equilibrium position is $x_{eq}=\frac{b}{a}$.

Q.

A uniform chain of mass m and length l overhangs a table with its two third part on the table.Find the work to be done, by a person to put the hanging part back on the table.

Q.

A block of mass 1 kg is placed at the point A of a rough track shown in figure (8-E6). If slightly pushed towards right, it stops at the point .8 of the track. Calculate the work done by the frictional force on the block during its transit from A to B.

Q. In the figure shown, the coefficient of static friction between $C$ and ground is $0.5$, coefficient of static friction between $A$ and $B$ is $0.25$, coefficient of static friction between $B$ and $C$ is zero. The minimum value of force $F$ (in Newton), to cause sliding between $A$ and $B$ is (Masses of $A,B$ and $C$ are respectively $2kg,4kg$ and $5kg$).

Q.

A block weighing 10 N travels down a smooth curved track AB joined to a rough horizontal surface (figure 8-E5). The rough surface has a friction coefficient of e20 with the block. If the block starts slipping on the track from a point 1'0 in above the horizontal surface, how far will it move on the rough surface ?

Q. A body of mass 2kg moves under the influence of a force. Its position x changes with time according to the relation $x=\frac{t^3}{3}$ where x is in meter and t in seconds. The work done by this force in first two seconds will be

1. 160 Joule
2. 16 Joule
3. 1.6 Joule
4. 1600 Joule

Q.

Potential energy of a particle is related to $x$ coordinate by equation $x^2-2x$will be equilibrium at

1. $x=0.5$

2. $x=2$

3. $x=1$

4. $x=4$

Q. The potential energy of a particle in a certain field has the form $U=\frac{a}{r^2}-\frac{b}{r},$ where $a$ and $b$ are postive constants, $r$ is the distance from the centre of the field.

1. the value of $r_0$ corresponding to the equilibrium position of the particle is $\frac{a}{b}$
2. Particle is in unstable equiltibrium.
3. the minimum attractive force is $-\frac{b^2}{27a^3}$
4. the value of $r_0$ corresponding to the equilibrium position of the particle is $\frac{2a}{b}$