A body is displaced from (0,0) to (1m,1m) along the path x=y by a force $F=\left(x^2\hat{j}+y\hat{i}\right)N$. The work done by this force will be :

1. $\frac{4}{3}J$

2. $\frac{5}{6}J$

3. $\frac{3}{2}J$

4. $\frac{7}{5}J$

When a body moves with a constant speed along a circle 

1. No work is done on it

2. No acceleration is produced in the body

3. No force acts on the body

4. Its velocity remains constant

A sphere of mass m is tied to end of a string of length l and rotated through the other end along a horizontal circular path with speed v. The work done by centripetal force in full horizontal circle is 

1. 0

2. $\left(\frac{{\displaystyle m{v}^2}}{{\displaystyle l}}\right)\hspace{0.17em}.\hspace{0.17em}2\pi l$

3. $\text{mg\hspace{0.17em}.\hspace{0.17em}2πl}$

4. $\left(\frac{{\displaystyle m{v}^2}}{{\displaystyle l}}\right)\hspace{0.17em}.\hspace{0.17em}\left(l\right)$

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

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

A particle moves from position ${\overrightarrow{r}}_1=3\hat{i}+2\hat{j}-6\hat{k}$ to position ${\overrightarrow{r}}_2=14\hat{i}+13\hat{j}+9\hat{k}$ under the action of force $4\hat{i}+\hat{j}+3\hat{k}N.$ The work done will be 

(1) 100 J

(2) 50 J

(3) 200 J

(4) 75 J

A particle moves under the effect of a force F = Cx from x = 0 to x = x₁. 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

A force \(F = -k(y\hat i +x\hat j)\) (where \(k\) is a positive constant) acts on a particle moving in the \(xy\text-\)plane. Starting from the origin, the particle is taken along the positive \(x\text-\)axis to the point \((a,0)\) and then parallel to the \(y\text-\)axis to the point \((a,a)\). The total work done by the force on the particle is:
1. \(-2ka^2\)
2. \(2ka^2\)
3. \(-ka^2\)
4. \(ka^2\)

The relationship between force and position is shown in the given figure (in a one-dimensional case). The work done by the force in displacing a body from \(x = 1~\text{cm}\) to \(x = 5~\text{cm}\) is:
      
1.   \(20~\text{ergs}\) 
2.   \(60~\text{ergs}\)
3.   \(70~\text{ergs}\) 
4.   \(700~\text{ergs}\)

Adjacent figure shows the force-displacement graph of a moving body, the work done in displacing body from x = 0 to x = 35 m is equal to-

(1) 50 J

(2) 25 J

(3) 287.5 J

(4) 200 J