A body constrained to move along the \(\mathrm{z}\)-axis of a coordinate system is subjected to constant force given by \(\vec{F}=-\hat{i}+2 \hat{j}+3 \hat{k}\) where \(\hat{i},\hat{j} \) and \(\hat{k}\) are unit vectors along the \(\mathrm{x}\)-axis, \(\mathrm{y}\)-axis and \(\mathrm{z}\)-axis of the system respectively. The work done by this force in moving the body a distance of \(4\) m along the \(\mathrm{z}\)-axis will be:
1. \(15\) J
2. \(14\) J
3. \(13\) J
4. \(12\) J

A block of mass \(m\) is being lowered by means of a string attached to it. The system moves down with a constant velocity. Then:
                                         
1. Work done by gravity on the block is positive.

2. Work done by F (the force of the string) on the block is negative.

3. Work done by gravity is equal in magnitude to that done by the string.

4. All of the above are true.

A rigid body of mass \(\mathrm{m}\) is moving in a circle of radius \(\mathrm{r}\) with constant speed \(\mathrm{v}.\) The force on the body is $\frac{{\mathrm{mv}}^2}{\mathrm{r}}$ and is always directed towards the center. The work done by this force in moving the body over half the circumference of the circle will be:
1. $\frac{{\mathrm{mv}}^2}{\mathrm{r\pi }}$ 
2. ${\mathrm{mr}}^2\mathrm{\pi }$
3. zero
4. $2{\mathrm{mv}}^2\mathrm{\pi }$

The kinetic energy of a body is increased by 21%. The percentage increase in the magnitude of linear momentum of the body will be:

1.  10%

2.  20%

3.  Zero

4.  11.5%

A person-1 stands on an elevator moving with an initial velocity of 'v' & upward acceleration 'a'. Another person-2 of the same mass m as person-1 is standing on the same elevator. The work done by the lift on the person-1 as observed by person-2 in time 't' is:

1.  $\mathrm{m}\left(\mathrm{g}\right)$ $+$ $\mathrm{a}\left(\mathrm{vt}\right)$ $+$ $\frac{1}{2}{\mathrm{at}}^2$

2.  $-\mathrm{mg}\left(\mathrm{vt}\right)$ $+$ $\frac{1}{2}{\mathrm{at}}^2$

3.  0

4.  $\mathrm{ma}\left(\mathrm{vt}\right)$ $+$ $\frac{1}{2}{\mathrm{at}}^2$

A block of mass m is placed in an elevator moving down with an acceleration $\frac{\mathrm{g}}{3}$. The work done by the normal reaction on the block as the elevator moves down through a height h is:

1.  $\frac{-2\mathrm{mgh}}{3}$

2.  $\frac{-\mathrm{mgh}}{3}$

3.  $\frac{2\mathrm{mgh}}{3}$

4.  $\frac{\mathrm{mgh}}{3}$

In the diagram shown, force F acts on the free end of the string. If the weight W moves up slowly by distance h, then work done on the weight by the string holding it will be: (Pulley and string are ideal)

1. Fh

2. 2Fh

3. $\frac{Fh}{2}$

4. 4Fh

The position-time graph of a particle of mass 2 kg is shown in the figure. Total work done on the particle from t = 0 to t = 4s is:
      

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 \(x = 1\) cm to \(x = 5\) cm is:

1.   \(20\) ergs
2.   \(60\) ergs
3.   \(70\) ergs
4.   \(700\) ergs

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