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%