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
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 where . 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:
1. | \(\sqrt{2 g h} \) | 2. | \(\sqrt{\frac{2 F h}{m}} \) |
3. | \(\sqrt{2 g h+\frac{2 F h}{m}} \) | 4. | \(\sqrt{2 g h-\frac{2 \sqrt{2} F h}{m}}\) |
The diagram represents a particle's potential energy curve 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.
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:
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 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. | \(1 \mathrm{~m} / \mathrm{s} \) | 2. | \(4 \mathrm{~m} / \mathrm{s} \) |
3. | \(2 \mathrm{~m} / \mathrm{s} \) | 4. | \(2 \sqrt{2} \mathrm{~m} / \mathrm{s}\) |