The displacement \(x\) of a particle varies with time \(t\) as \(x=ae^{-\alpha t}+be^{\beta t}\) where \(a,b,\alpha\) and \(\beta\) are positive constants. The velocity of the particle will:
1. decrease with time
2. be independent of \(\alpha\) and \(\beta\)
3. drop to zero when \(\alpha=\beta\)
4. increase with time
A transformer having an efficiency of \(75\%\) is working on \(220~\mathrm{V}\) and \(4.4~\mathrm{kW}\) power supply. If the current in the secondary coil is \(5~\mathrm{A}\). What will be the voltage across the secondary coil and the current in the primary coil?
1. \(
V_s=220 \mathrm{~V}, I_p=20 \mathrm{~A}
\)
2. \( V_s=660 \mathrm{~V}, I_p=15 \mathrm{~A}
\)
3. \( V_s=660 \mathrm{~V}, I_p=20 \mathrm{~A}
\)
4. \( V_s=220 \mathrm{~V}, I_p=15 \mathrm{~A}\)
1. \( 10 \mathrm{~m} / \mathrm{s} \)
2. \( 8 \mathrm{~m} / \mathrm{s} \)
3. \( 6 \mathrm{~m} / \mathrm{s} \)
4. \( 9 \mathrm{~m} / \mathrm{s}\)
One mole of a monoatomic ideal gas undergoes the process \(A\rightarrow B\) in the given \(P-V\) diagram. The molar heat capacity for this process is:
1. \(\frac{3R}{2}\)
2. \(\frac{13R}{6}\)
3. \(\frac{5R}{2}\)
4. \(2R\)
1. \(5.5 \mathrm{~cm} \)
2. \(3.8 \mathrm{~cm} \)
3. \(2.7 \mathrm{~cm} \)
4. \(1.3 \mathrm{~cm}\)
A cylinder of radius \(R\) and length \(L\) is placed in a uniform electric field \(E\) parallel to the cylinder axis. The total flux for the surface of the cylinder is given by:
1. \(2\pi R^2E\)
2. \(\frac{\pi R^2}{E}\)
3. \(\frac RE\)
4. zero
If A + B = C and that C is perpendicular to A. What is the angle between A and B, if |A| = |C|?
1. \(\frac{\pi}{4}~\text{rad}\)
2. \(\frac{\pi}{2}~\text{rad}\)
3. \(\frac{3\pi}{4}~\text{rad}\)
4. \(\pi~\text{rad}\)
1. \( 2 \mathrm{~m} / \mathrm{s} \)
2. \( 3 \mathrm{~m} / \mathrm{s} \)
3. \( 3.25 \mathrm{~m} / \mathrm{s} \)
4. \( 4.25 \mathrm{~m} / \mathrm{s}\)
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