Q. No.1. \(45^{\circ} \)
2. \(90^{\circ} \)
3. \(-45^{\circ} \)
4. \(180^{\circ}\)
If a vector \(2\hat{i}+3\hat{j}+8\hat{k}\) is perpendicular to the vector \(-4\hat{i}+4\hat{j}+\alpha \hat{k},\) then the value of \(\alpha\) will be:
1. \(-1\)
2. \(\frac{-1}{2}\)
3. \(\frac{1}{2}\)
4. \(1\)
A block of \(1\) kg is released from the top of a smooth curve \(\mathrm{AB},\) and then it encounters a rough surface \(\mathrm{BC},\) coming to rest at \(\mathrm{C}.\) The work done by friction is:
(take \(g=10\) m/s2)
| 1. | \(25\) J | 2. | \(50\) J |
| 3. | \(-25\) J | 4. | \(-50\) J |
The work done by all the forces (external and internal) on a system equals the change in:
| 1. | total energy | 2. | kinetic energy |
| 3. | potential energy | 4. | none of these |
1. \(30\) cm
2. \(27\) cm
3. \(24\) cm
4. \(28\) cm
A body of mass \(1\) kg is thrown upwards with a velocity \(20\) ms-1. It momentarily comes to rest after attaining a height of \(18\) m. How much energy is lost due to air friction?
(Take \(g=10\) ms-2)
1. \(20\) J
2. \(30\) J
3. \(40\) J
4. \(10\) J
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 |
| 1. | zero | 2. | \(-\frac12mu^2\cos^2\theta\) |
| 3. | \(-\frac12mu^2\sin^2\theta\) | 4. | \(-\frac12mu^2\) |
1. \(200~\text J\)
2. \(-200~\text J\)
3. \(1000~\text J\)
4. \(-1000~\text J\)
A body of mass \(0.5~\text{kg}\) travels in a straight line with velocity \(v=ax^{3/2}\) where \(a=5~\text{m}^{-1/2}\text{s}^{-1}\). The work done by the net force during its displacement from \(x=0~\text{m}\) to \(x=2~\text{m}\) is:
1. \(15~\text{J}\)
2. \(50~\text{J}\)
3. \(10~\text{J}\)
4. \(100~\text{J}\)
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