- 1(current)
Q. No.1. \(1:2\)
2. \(1:1\)
3. \(\sqrt{2}:1\)
4. \(1:\sqrt{2}\)
A rope of uniform mass per unit length \(\mu\) is suspended from the ceiling, hanging under its own weight. If a small transverse pulse is formed at its lower end A, it travels upward with a local speed \(v=\sqrt{\frac{tension}{mass/length}}\).
The speed of the pulse is:
| 1. | maximum at A, minimum at O |
| 2. | minimum at A, maximum at O |
| 3. | uniform |
| 4. | minimum at A and O, maximum in the middle |
| 1. | \({ 1 \over 2L} \sqrt {T\over m}~~~~~~~~~~~~~~\) | 2. | \(\frac{1}{4 L} \sqrt{\frac{T}{m}}~~~~~~~~~~~~~~\) |
| 3. | \(\frac{1}{2} \sqrt{\frac{TL}{2m}}\) | 4. | \(\frac{1}{2} \sqrt{\frac{T}{m L}}\) |
A steel wire \(0.72~\text{m}\) long has a mass of \(5\times10^{-3}~\text{kg}\).
If the wire is under tension of \(60~\text{N}\), the speed of transverse waves on the wire will be:
1. \(85~\text{m/s}\)
2. \(83~\text{m/s}\)
3. \(93~\text{m/s}\)
4. \(100~\text{m/s}\)
A wave travelling along a string is described by, \(y(x,~t)=0.005 \mathrm{sin}(80.0x-3.0t),\) in which the numerical constants are in SI units. The displacement \(y\) of the wave at a distance \(x = 30.0\) cm and time \(t=20\) s is:
1. \(0.5\) mm
2. \(5\) mm
3. \(5\) m
4. \(5\) cm
- 1(current)
Q. No.
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