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.
2.
3.
4. \(1\)
A block of \(1\) kg is released from a top of a smooth curve AB, and then it encounters a rough surface BC, coming to rest at C. The work done by friction is: (\(g=10\) 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. | \(-\frac12mu^2cos^2\theta\) |
| 3. | \(-\frac12mu^2sin^2\theta\) | 4. | \(-\frac12mu^2\) |
1. \(200\) J
2. \(-200\) J
3. \(1000\) J
4. \(-1000\) J
A body of mass \(0.5\) kg travels in a straight line with velocity \(v=ax^{3/2}\) where \(a=5~\mathrm{m^{-1/2}s^{-1}}\). The work done by the net force during its displacement from \(x=0\) m to \(x=2\) m is:
1. \(15\) J
2. \(50\) J
3. \(10\) J
4. \(100\) J
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