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. | \(\sqrt{2 g h-\frac{2 \sqrt{2} F h}{m}}\) |
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
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 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
A particle moves with a velocity of m/s under the influence of a constant force N. The instantaneous power applied to the particle is:
1. | 200 J/s | 2. | 40 J/s |
3. | 140 J/s | 4. | 170 J/s |
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:
1. | 8 J | 2. | 4 J |
3. | 0 J | 4. | Can't be determined |
A particle of mass 'm' is projected at an angle ' with the horizontal, with an initial velocity 'u'. The work done by gravity during the time it reaches its highest point is:
1.
2.
3.
4.
The potential energy of a particle varies with distance r as shown in the graph. The force acting on the particle is equal to zero at:
1. | P | 2. | S |
3. | Both Q and R | 4. | Both P and S |
A block of mass m is placed in an elevator moving down with an acceleration . The work done by the normal reaction on the block as the elevator moves down through a height h is:
1.
2.
3.
4.
A particle is moving such that the potential energy U varies with position in metre as U (x) = ( - 2x + 50) J. The particle will be in equilibrium at:
1. x = 25 cm
2. x = 2.5 cm
3. x = 25 m
4. x = 2.5 m