Work Done When Path Is Not Straight

Q.

Force F on a particle moving in a straight line varies with displacement d as shown in the figure. The work done on the particle during its displacement of 12 m is:

1. 21J

2. 26J

3. 13J

4. 18J

Q. The force $F$ acting on a particle of mass ${}^{\prime }{m}^{\prime }$ is indicated by the force - time graph shown below. The change in momentum of the particle over the time interval from zero to $8\text{s}$ is

1. $24\text{N s}$
2. $20\text{N s}$
3. $12\text{N s}$
4. $6\text{N s}$

Q.

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

1. $20\sqrt{2}m/s$

2. $20\sqrt{3}m/s$

3. $40m/s$

4. Zero

Q. A particle is moved from $(0,0)$ to $(a,a)$ under a force $\overrightarrow{F}=(3\hat{i}+4\hat{j})$ from two paths. Path $1$ is $OP$ and path $2$ is $OQP$. Let $W_1$ and $W_2$ be the works done by this force along two paths. Then

1. $W_1=W_2$
2. $W_2=4W_1$
3. $W_1=2W_2$
4. $W_2=2W_1$

Q. A uniform chain is held on a frictionless table with one third of its length hanging over the edge.if the chain has a length L and mass M, how much work is required to pull the Hanging part back on the table.

Q. An object of mass 5 kg is acted upon by a force that varies with position of the object as shown. If the object starts out from rest at a point x = 0, what is its speed at x = 50 m?

1. $12.2m{s}^{-1}$
2. $18.2m{s}^{-1}$
3. $16.4m{s}^{-1}$
4. $20.4m{s}^{-1}$

Q.

You lift a suitcase from the floor and keep it on a table. The work done by you on the suitcase depends on

1. the path taken by the suitcase

2. the time taken by you in doing so

3. the weight of the suitcase

4. your weight

Q. Three point masses each of mass ${}^{\prime }{m}^{\prime }$ are kept at three vertices of a square of side ${}^{\prime }{a}^{\prime }$ as shown in figure. Find gravitational field strength at point $\text{O}$.

1. $\sqrt{2}\frac{Gm}{a^2}$, towards $\text{B}$
2. $(\sqrt{2}+\frac{1}{2})\frac{Gm}{a^2}$, towards $\text{O}$
3. $(\sqrt{2}+\frac{1}{2})\frac{Gm}{a^2}$, towards $\text{B}$
4. None of the above

Q.

Explain any one case when no work is done by a force.

Q. Two bodies A and B of masses $m$ and $2m$ respectively are kept a distance $d$ apart. Where should a small particle be placed, so that the net gravitational force on it due to the bodies A and B is zero?

1. $\frac{d}{(1+\sqrt{2})}$
2. $\frac{d}{(1-\sqrt{2})}$
3. $\frac{d}{(1+\sqrt{3})}$
4. $\frac{2d}{(1+\sqrt{3})}$

Q.

A block of mass 2kg is released from A on the track that is one quadrant of a circle of radius 1m. It slides down the track and reaches B with a speed of and finally stops at C at a distance of 3m from . The work done against the force of friction is

1. 10 J

2. 20 J

3. 2 J

4. 6 J

Q. A force acts on a $3\text{gm}$ 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 $4$ second is

1. $576\text{mJ}$
2. $450\text{mJ}$
3. $490\text{mJ}$
4. $528\text{mJ}$

Q. Four point masses each of mass ${}^{\prime }{m}^{\prime }$ are placed at four vertices $\text{A, B, C}$ and $\text{D}$ of a regular hexagon of side ${}^{\prime }{a}^{\prime }$ as shown in figure. Find the gravitational field strength at the centre $\text{O}$ of the hexagon.

1. $\frac{\sqrt{3}Gm}{a^2}$
2. $\frac{\sqrt{2}Gm}{a^2}$
3. $\frac{\sqrt{3}Gm}{2a^2}$
4. $\frac{Gm}{a^2}$

Q. Two point masses $m$ and $4m$ are separated by a distance $d$ on a line. A third point mass $m_0$ is to be placed at a point on the line such that the net gravitational force on it is zero. The distance of that point from the mass $m$ is

1. $\frac{d}{2}$
2. $\frac{d}{4}$
3. $\frac{d}{3}$
4. $\frac{d}{5}$

Q. Two point masses $m$ and $4m$ are separated by a distance $d$ on a straight line as shown in figure. A third point mass $m_o$ is to be placed at a point on the line such that the net gravitational force on it is zero.


The distance of the $m_0$ from the $m$ is

1. $\frac{d}{2}$
2. $\frac{d}{4}$
3. $\frac{d}{3}$
4. $\frac{d}{5}$

Q. A particle of mass $13\text{kg}$ moves with $5\text{m/s}$ in $y-z$ plane along the path $5y=12z+60$. Here $y$ and $z$ are in metre. Magnitude of angular momentum of the particle about origin (in ${\text{kg m}}^2{\text{s}}^{-1}$), when the particle is at $z=10\text{m}$, is

[Your answer must be an integer]

Q. Many identical point masses $m$ are placed along $x-$axis, at $x=0,1,2,4,....$. The magnitude of gravitational force on mass at origin $(x=0)$ will be

1. $G{m}^2$
2. $\frac{4}{3}G{m}^2$
3. $\frac{2}{3}G{m}^2$
4. $\frac{5}{4}G{m}^2$

Q. You lift a Suitcase from the floor and keep it on a table.The work done by you on the suitcase does not depend on

1. the path taken by the suitcase.
2. the time taken by you in doing so.
3. the weight of the suitcase.
4. your weight.

Q.

A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by

Where are unit vectors along the x-, y- and z-axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the z-axis?

Q. Three point masses each of same mass M are placed at the corners of an equilateral triangle as shown. A fourth point mass m is placed at the centroid O of the triangle. The gravitational constant is G. Choose correct statements. [Consider the mutual gravitational forces of the four given masses only]

1. Escape velocity of m is, $v_e=\sqrt{\frac{2\sqrt{3}GM}{l}}$
2. Escape velocity of m is, $v_e=\sqrt{\frac{6\sqrt{3}GM}{l}}$
3. At a point on the line passing through O and perpendicular to plane of triangle net force on m is along negative z-axis or positive z-axis
4. Escape velocity of m is, $v_e=\sqrt{\frac{3GM}{l}}$

Q.

Why is a porter carrying a load on his load, but standing in one place, does not work?

Q.

How do you calculate escape velocity from the gravitational force?

Q. A small body of mass $m=0.10kg$ moves in the reference frame rotating about a stationary axis with constant angular velocity $\omega =5.0rad/s$. What work does the centrifugal force of inertia perform during the transfer of this body along an arbitrary path from point $1$ to point $2$ which are located at the distance $r_1=30cm$ and $r_2=50cm$ from the axis of rotation?

1. $0.15J$
2. $0.4J$
3. $0.2J$
4. $0.35J$

Q. A particle is displaced from point $\text{A}(1,2,3)$ to $\text{B}(1,3,4)$ under action of two constant forces ${\overrightarrow{F}}_1=$$\hat{i}+2\hat{j}+\hat{k}$ and ${\overrightarrow{F}}_2=$$\hat{i}+\hat{j}$. Find the total work done on the particle to move it from point $\text{A}$ to $\text{B}$.

1. $2\text{J}$
2. $3\text{J}$
3. $4\text{J}$
4. $5\text{J}$

Q.

A boy pushes a box with a force of 10 N and moves it through a distance of 10 m in 5 seconds. Find the work done by the boy?

Q.

Give three situations in which a force produces displacement but still, the work done by the force is zero.

Q. A particle of mass $13\text{kg}$ moves with $5\text{m/s}$ in $y-z$ plane along the path $5y=12z+60$. Here $y$ and $z$ are in metre. Magnitude of angular momentum of the particle about origin (in ${\text{kg m}}^2{\text{s}}^{-1}$), when the particle is at $z=10\text{m}$, is

[Your answer must be an integer]

Q. A particle of mass $0.5\text{kg}$ travels in a straight line with velocity $v=a{x}^{3/2}$, where $a=5$. What is the work done in joules by the net force during its displacement from $x=0$ to $x=2\text{m}$ ?

Q. The work done by the frictional force on a surface in drawing a circle of radius r on the surface by a pencil of negligible mass with a normal pressing force N (coefficient of friction ${\mu }_k$) is?

1. $-2\pi r{\mu }_{k}N$
2. $-2\pi r^2{\mu }_{k}N$
3. $4\pi r^2{\mu }_{k}N$
4. $-3\pi r^2{\mu }_{k}N$

Q. How many nuclei of ${}_{92}{U}^{235}$ should undergo fission, per second, to produce a power of $10MW$, if $200MeV$ of energy is released per fission of ${}_{92}{U}^{235}$?

1. $3.12500$
2. $3.125\times {10}^7$
3. $3.125\times {10}^{17}$
4. $3.125\times {10}^{27}$