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

$\mathrm{1.\; 15} J$

$\mathrm{2.\; 14} J$

$\mathrm{3.\; 13} J$

$\mathrm{4.\; 12} J$

The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?

1. 2.5 m/s

2. 3.9 m/s

3. 4.7 m/s

4. 5.3 m/s

A body of mass 0.5 kg travels in a straight line with velocity $\mathrm{v}={\mathrm{ax}}^{3/\mathrm{2 }}$where $\mathrm{a}=5 {\mathrm{m}}^{-1/2} {\mathrm{s}}^{-1}$. What is the work done by the net force during its displacement from x = 0 to x = 2 m?

1. 50 J

2. 45 J

3. 68 J

4. 90 J

A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down at a uniform speed of 7 m/s. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact?

1.  8.82 J

2.  7.65 J

3.  7.01 J

4.  7.98 J

A body of mass 'm' is released from the top of a fixed rough inclined plane as shown in the figure. If the frictional force has magnitude F, then the body will reach the bottom with a velocity: $(\mathrm{L}=\sqrt{2}\mathrm{h})$

1. $\sqrt{2gh}$

2. $\sqrt{\frac{2Fh}{m}}$

3. $\sqrt{2gh+\frac{2Fh}{m}}$

4. $\sqrt{2gh-\frac{2\sqrt{2}Fh}{m}}$

The given diagram represents the potential energy curve of a particle in a field. The particle will be in equilibrium at which position(s):

1. B and D

2. A and C

3. A, B, and C

4. A, B, C, and D

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 potential energy of a system increases if work is done:

1. by the system against a conservative force.

2. by the system against a non-conservative force.

3. upon the system by a conservative force.

4. upon the system by a non-conservative force.

The potential energy of a 1 kg particle free to move along the x-axis is given by:

$\mathrm{U}\left(\mathrm{x}\right) = \left(\frac{{\mathrm{x}}^4}{4}-\frac{{\mathrm{x}}^2}{2}\right)\mathrm{J}$

The total mechanical energy of the particle is 2J. Then, the maximum speed (in ms^-1) will be
1. \(3 \over \sqrt{2} \)
2. \(\sqrt{2}\)
3. \(1 \over \sqrt{2}\)
4. 2

The power supplied to a particle of mass 2 kg varies with time as $\mathrm{P}=\frac{3{\mathrm{t}}^2}{2}$ Watt, where t is in seconds. If the velocity of a particle at t = 0 is v = 0, then the velocity of the particle at t = 2 s will be:

1. 1 m/s

2. 4 m/s

3. 2 m/s

4. $2\sqrt{2}$ m/s