Work Done When Force Is Varying

Q.

If the force and displacement of a particle in direction of force are doubled. Work would be

1. Double

2. $4$ times

3. Half

4. $\frac{1}{4}$ times

Q.

A force of $5N$ acts on a $15kg$ body initially at rest. The work done by the force during the first second of motion of the body is

1. $5J$

2. $\frac{5}{6}J$

3. $6J$

4. $75J$

Q.

A particle moves under the effect of a force F = Cx from x = 0 to $x=x_1$ . The work done in the process is

1. $C{x}_1^2$

2. $\frac{1}{2}C{x}_1^2$

3. $C{x}_1$

4. Zero

Q. A force $F$ acting on a particle varies with the position $x$ as shown in figure. The work done by this force in displacing the particle from $x=-2m$ to $x=0$.

1. $+10\text{J}$
2. $+20\text{J}$
3. $-20\text{J}$
4. $-10\text{J}$

Q. An object is displaced from position ${\overrightarrow{r}}_1=\hat{i}+2\hat{j}\text{m}$ to $\overrightarrow{r_2}=2\hat{i}+4\hat{j}\text{m}$ under the action of force $\overrightarrow{F}=(6x^2\hat{i}+4y\hat{j})\text{N}$. Find the work done by this force.

1. $76\text{J}$
2. $46\text{J}$
3. $19\text{J}$
4. $38\text{J}$

Q. A force $\overrightarrow{F}=-k(y\hat{i}+x\hat{j})$ (where $k$ is a positive constant) acts on a particle moving in the $x-y$ 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 point $(a,a)$. Then, total work done by the force is

1. $-2k{a}^2$
2. $2k{a}^2$
3. $-k{a}^2$
4. $k{a}^2$

Q.

A position dependent force $F=7-2x+3x^2$ acts on a small body of mass 2 kg and displaces it from x = 0 to x = 5m. The work done in joules is

1. 70

2. 270

3. 35

4. 135

Q. A wooden block is floating partially immersed in a water tank. If the block is pressed slowly to bottom of the tank by a force $F$, work done by this $F$ is equal to:

1. Work done against upthrust exerted by the water
2. Work done against upthrust plus loss of gravitational potential energy of the block.
3. Work done against upthrust minus loss of gravitational potential energy of the block.
4. All of the above.

Q. A force $\overrightarrow{F}=(2x\hat{i}+3y^2\hat{j})\text{N}$ acts on a body and displaces it from the origin $(0,0)$ to $(2\text{m},4\text{m})$.The work done (in $\text{J}$) by the force is

Q. A force varying with displacement$\left(x\right)$ is given as $F=a{e}^{-bx}$ acts on a particle of mass $m$ moving in a straight line. Find the work done on the particle in its displacement from origin to a distance $d$.

1. $\frac{a}{b}(1-2e^{-bd})$
2. $\frac{a}{b}(2-e^{-bd})$
3. $\frac{a}{b}(1-e^{-bd})$
4. $\frac{2a}{b}(2-e^{-bd})$

Q. A carpenter is applying a force $\overrightarrow{F}=-1.5x{y}^2\hat{j}$ on a hammer, whose magnitude depends on the position of the tool. The displacement of the tool from the origin to the point $(2,2)\text{m}$. Find the workdone on the hammer, if the displacement is along the straight line $y=x$.

1. $16\text{J}$
2. $6\text{J}$
3. $0\text{J}$
4. $12\text{J}$

Q. A varying force is given as
$F=\left\{\begin{array}{cc}4\text{N}& 0\le x\le 6\\ 6x\text{N}& 6<x\le 10\\ 3x^2\text{N}& 10<x\le 20\end{array}\right\}$ (where $x$ is meters)
Find the total work done by this force to displaces from $x=4$ to $x=15$ metres.

1. $0$
2. $2000\text{J}$
3. $2500\text{J}$
4. $2575\text{J}$

Q. A $5.0\text{kg}$ block moves in a straight line on a horizontal frictionless surface under the influence of a force that varies with position as shown in figure. How much work done by the force as the block moves from the origin to $x=8\text{m}$?

1. $30\text{J}$
2. $16\text{J}$
3. $46\text{J}$
4. $14\text{J}$

Q.

Given $\overrightarrow{F}=\left(x{y}^2\right)\hat{i}+\left(x^{2}y\right)\hat{j}N$. The work done by $\overrightarrow{F}$ when a particle is taken along the semicircular path OAB where the coordinates of B are (4, 0) is

1. $\frac{65}{3}J$

2. $\frac{75}{2}J$

3. $\frac{73}{4}J$

4. Zero

Q.

The distance $x$ moved by a body of mass 0.5 kg due to a force varies with time $t$ as
$x=3t^2+4t+5$
where $x$ is expressed in metre and t in second. What is the work done by the force in the first 2 seconds?

1. 25 J

2. 50 J

3. 75 J

4. 100 J

Q.

The distance $x$ moved by a body of mass 0.5 kg due to a force varies with time $t$ as
$x=3t^2+4t+5$
where $x$ is expressed in metre and t in second. What is the work done by the force in the first 2 seconds?

1. 25 J

2. 50 J

3. 75 J

4. 100 J

Q. A force $F=5+2x+3x^2$ acts on a particle in $x$ direction where $F$ is in Newton and $x$ is in meter . Find the workdone by this force during a displacement from $x=1\text{m}$ to $x=2\text{m}$.

1. $15\text{J}$
2. $12\text{J}$
3. $32\text{J}$
4. $-15\text{J}$

Q. A force $F$ is acting on an object varies with distance $x$ is shown in the figure given below. The force is in $\text{N}$ and $x$ is in $\text{m}$. The work done by the force in moving the object from $x=0\text{to}x=6\text{m}$ is

1. $4.5\text{J}$
2. $13.5\text{J}$
3. $9.0\text{J}$
4. $18\text{J}$

Q. A body of mass 6kg is under a force which causes displacement in it given by $S=\frac{t^2}{4}$ metres where t is time. The work done by the force in 2 seconds is

1. 12 J
2. 9 J
3. 6 J
4. 3 J

Q.

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

1. 
   

2. 
   

3. 
   

4. 
   

Q. A body of mass 6kg is under a force which causes displacement in it given by $S=\frac{t^2}{4}$ metres where t is time. The work done by the force in 2 seconds is

1. 12 J
2. 9 J
3. 6 J
4. 3 J

Q. In case of a variable force, total work is calculated by summation of work done during very small displacements.

1. False
2. True

Q. A small mass starts sliding down a fixed inclined plane of inclination ${45}^{\circ }$ with the horizontal. The coefficient of friction is $\mu ={\mu }_{0}x$ where $x$ is the distance through which the mass slides down and ${\mu }_0$ is a constant. Find the heat produced during half the distance travelled by the particle before it stops.

1. $\frac{mg}{\sqrt{2}{\mu }_0}$
2. $\frac{mg}{2\sqrt{2}{\mu }_0}$
3. $\frac{mg}{{\mu }_0}$
4. $\frac{mg}{2{\mu }_0}$

Q. A varying force is given as
$F=\left\{\begin{array}{cc}4\text{N}& 0\le x\le 6\\ 6x\text{N}& 6<x\le 10\\ 3x^2\text{N}& 10<x\le 20\end{array}\right\}$ (where $x$ is meters)
Find the total work done by this force to displaces from $x=4$ to $x=15$ metres.

1. $0$
2. $2000\text{J}$
3. $2500\text{J}$
4. $2575\text{J}$

Q.

A force $F=-K(y\hat{i}+x\hat{j})$, where K is a positive constant, acts on a particle moving in the x-y 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 particle is

1. $-2K{a}^2$

2. $2K{a}^2$

3. $-K{a}^2$

4. $K{a}^2$