The minimum work done in pulling up a block of wood weighing \(2\) kN for a length of \(10\) m on a smooth plane inclined at an angle of \(15^\circ\) with the horizontal is (given: \(\mathrm{sin}15^\circ=0.2588)\):
1. \(4.36\) kJ
2. \(5.17\) kJ
3. \(8.91\) kJ
4. \(9.82\) kJ
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.
2.
3. 0
4.
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 moves from a point to when a force of N is applied. How much work has been done by the force?
1. | 8 J | 2. | 11 J |
3. | 5 J | 4. | 2 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 position of a particle (x) varies with time (t) as \(x = (t - 2)^2\), where x is in meters and t is in seconds. Calculate the work done during t = 0 to t = 4 s if the mass of the particle is 100 g.
1. 0.4 J
2. 0.2 J
3. 0.8 J
4. Zero
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 bicyclist comes to a skidding stop in \(10\) m. During this process, the force on the bicycle due to the road is \(200\) N is directly opposed to the motion. The work done by the cycle on the road is:
1. | \(+2000\) J | 2. | \(-200\) J |
3. | zero | 4. | \(-20000\) J |
A cord is used to vertically lower a block of mass m by a distance d at a constant downward acceleration of . The work done by the chord on the block will be:
1. mgd
2. -mgd
3. mgd
4. -mgd
Forces acting on a particle have magnitudes of 14, 7, and 7 N and act in the direction of vectors \(6\hat{i} + 2\hat{j} + 3\hat{k}\), \(3\hat{i} - 2\hat{j} + 6\hat{k}\), \(2\hat{i} - 3\hat{j} - 6\hat{k}\) respectively. The forces remain constant while the particle is displaced from point A: (2, –1, –3) to B: (5, –1, 1). The coordinates are specified in meters. The work done equal to:
1. | 75 J | 2. | 55 J |
3. | 85 J | 4. | 65 J |