Work Done When Force Is Varying

Q.

When a rubber band is stretched by a distance x, it exerts a restoring force of magnitude $F=ax+b{x}^2$, where a and b are constants. The work done in stretching the upstretched rubber band by L is

1. $a{L}^2+b{L}^3$

2. $\frac{1}{2}(a{L}^2+b{L}^3)$

3. $\frac{a{L}^2}{2}+\frac{b{L}^3}{3}$

4. $\frac{1}{2}(\frac{a{L}^2}{2}+\frac{b{L}^3}{3})$

Q. Three constant forces F1 = 2i-3j+2k, F2 = i+j-k, and F3 = 3i+j-2k in newtons displace a particle from (1, -1, 2) to (-1, -1, 3) and then to (2, 2, 0) (displacement being measured in meteres). Find the total work done by the forces.

Q. The work done in moving a particle from a point(1, 1) to (2, 3) in a plane in force field with potentialU=K(x + y) is(1) 3k(2) -3k(3) k(4) Zeroth rown from ground with speed

Q. A force F = (5 + 2x) acts on a particle in x direction, where F is in newton and x is in metreFind the work done by this force during a displacement from x = 0 to x = 1 m.

Q.

A metallic wire of length L metres extends by l metres when stretched by suspending a weight Mg to it. The mechanical energy stored in the wire is

1. 

2. 

3. 

4. 

Q. 32. A force of 4x2+3x N acts on a particle which displaces it from x=2, to x=3 the work done by the force

Q.

The displacement x of a particle moving in one dimension under the action of a constant force is related to the time t by the equation, t = $\sqrt{x}$ + 3 where x is in meters and t is in seconds. The work done by the force in the first 6 seconds is

1. 9 J

2. 0 J

3. 3 J

4. 6 J

Q. A position dependent force F=ysquare x icap +xsquare y jcap acts on a particle and displace it from x = 1 m, y = 2 m to x = 2 m, y = 1 m. The work done by the force is Options: J 10 J 20 J Should have chosen Zero

Q. a force F=20N is acting on a partice in a direction making an angle 53 degree with x-axis. A particle koves from point (4, 5)to 1(10, -4). Find out Work done by the force.

Q. An object has a displacement from position vector \overrightarrow{r_1}=(2\oversetΛ i+3\oversetΛ j)m to \overrightarrow{r_2}=(4\oversetΛ i+6\oversetΛ j)m under a force \overrightarrow F=(3x^2\oversetΛ i+2y\oversetΛ j)N, then work done by the force is (1) 24 J (2) 33 J (3) 83 J (4) 45 J

Q. 2. Force acting on a particle is (2i + 3j) N. Work done by thisforce is zero, when a particle is moved on the line3y+kx = 5. Here value of k is(a) 2(b) 4(c) 6(d) 8CO

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 porter lifts a suitcase weighing $20kg$ from the platform and puts it on his head $2.0m$ above the platform. Calculate the work done by the porter on the suitcase.

1. 

2. 

3. 

4. None of these

Q. { A force acts on a }2 kg particle whose position is }}{ given by }x=(2t-t^2+3)m . The work done on the }}{ particle in first }4 s is

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. The position }x of a particle moving along }x -axis at }{ time }(t) is given by the equation }t=\sqrt x+2 , where }}x is metres and }t in seconds. Find the work } done by the force in first four seconds. } (1) Zero } (2) }2J (3) }4J (4) }8J

Q.

A body of mass 3 kg is under a force, which causes a displacement in it is given by $S=\frac{t^3}{3}$ (in m). Find the work done by the force in first 2 seconds

1. 2 J

2. 3.8 J

3. 5.2 J

4. 24 J

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 particle moves from a point (2m, 3m, 0) to (3m, 2m, 0) under the action of force of magnitude 5N acting along the line x=y . find the work done by the force on particle during this displacem

Q.

The relationship between force and position is shown in the figure given (in one dimensional case). The work done by the force in displacing a body from x = 1 cm to x = 5 cm is

1. 20 ergs

2. 60 ergs

3. 70 ergs

4. 700 ergs

Q. The force on a particle is directed along an $x$ axis and given by
$F=F_0(x/x_0-1).$ Find the work done by the force in moving the particle from $x=0$ to $x=2x_0$.

1. $2x_0(F_0-1)$
2. $x_0(F_0-1)$
3. $3x_0(F_0-1)$
4. $0$

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. Force $F$ on a particle moving in a straight line varies with distance $d$ as shown in the figure
The work done on the particle during its displacement of $12\text{m}$ is

1. $18\text{J}$
2. $21\text{J}$
3. $26\text{J}$
4. $13\text{J}$

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.

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 $\overrightarrow{F}=-k(y\hat{i}+x\hat{j})$ where $k$ is a positive constant acts on a particle moving in the xy-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 $\overrightarrow{F}$ on the particle is

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

Q. Force acting on a particle varies with displacement as shown in figure. The workdone by this force on the particle from $x=-8mtox=+8m$

1. $60\text{J}$
2. $-60\text{J}$
3. $100\text{J}$
4. $-100\text{J}$

Q. a particle moves from position 3i+2j-k to 14i+13j+9k dur to uniform force of (4i+j+3k)N. if the displacement in meters then work done will be-

Q. A particle moves from point P(1, 2, 3)m to Q(2, 1, 4)m under the action of a constant force F = (2i+j+k)N. Work done by the force is?

Q. A position dependent force F acting on a particleand its force-position curve is shown in the figure.The work done by force from x - 1 m to x 4 m20. A(N98+9120(w)xCO-20(1) 35 J(2) -20 J(3) -15 J(4) 20 J