A uniform conducting wire of length \(12a\) and resistance '\(R\)' is wound up as a current carrying coil in the shape of,
(i) | an equilateral triangle of side '\(a\)' |
(ii) | a square of side '\(a\)' |
The magnetic dipole moments of the coil in each case respectively are:
1. \(3Ia^2~\text{and}~4Ia^2\)
2. \(4Ia^2~\text{and}~3Ia^2\)
3. \(\sqrt{3}Ia^2~\text{and}~3Ia^2\)
4. \(3Ia^2~\text{and}~Ia^2\)
Two conducting circular loops of radii \(R_1\)\(R_2\) are placed in the same plane with their centres coinciding. If \(R_1>>R_2\) the mutual inductance \(M\) between them will be directly proportional to:
1. | \(\dfrac{R^2_1}{R_2}\) | 2. | \(\dfrac{R^2_2}{R_1}\) |
3. | \(\dfrac{R_1}{R_2}\) | 4. | \(\dfrac{R_2}{R_1}\) |
A ball of mass \(0.15~\text{kg}\) is dropped from a height \(10~\text{m}\), strikes the ground, and rebounds to the same height. The magnitude of impulse imparted to the ball is \((g=10 ~\text{m}/\text{s}^2)\) nearly:
1. \(2.1~\text{kg-m/s}\)
2. \(1.4~\text{kg-m/s}\)
3. \(0~\text{kg-m/s}\)
4. \(4.2~\text{kg-m/s}\)
Twenty seven drops of same size are charged at \(220~\text{V}\) each. They combine to form a bigger drop. Calculate the potential of the bigger drop:
1. \(1520~\text{V}\)
2. \(1980~\text{V}\)
3. \(660~\text{V}\)
4. \(1320~\text{V}\)
For the given circuit, the input digital signals are applied at the terminals \(A\), \(B\) and \(C\). What would be the output at terminal \(Y\)?
1. | |
2. | |
3. | |
4. |
A particle of mass \(m\) is projected with a velocity, \(v=kV_{e} ~(k<1)\) from the surface of the earth. The maximum height, above the surface, reached by the particle is: (Where \(V_e=\) escape velocity, \(R=\) radius of the earth)
1. | \(\dfrac{R^{2}k}{1+k}\) | 2. | \(\dfrac{Rk^{2}}{1-k^{2}}\) |
3. | \(R\left ( \dfrac{k}{1-k} \right )^{2}\) | 4. | \(R\left ( \dfrac{k}{1+k} \right )^{2}\) |
A car starts from rest and accelerates at \(5~\text{m/s}^{2}\). At \(t=4~\text{s}\), a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at \(t=6~\text{s}\)? (Take \(g=10~\text{m/s}^2)\)
1. \(20\sqrt{2}~\text{m/s}, 0~\text{m/s}^2\)
2. \(20\sqrt{2}~\text{m/s}, 10~\text{m/s}^2\)
3. \(20~\text{m/s}, 5~\text{m/s}^2\)
4. \(20~\text{m/s}, 0~\text{m/s}^2\)
A series LCR circuit containing \(5.0~\text{H}\) inductor, \(80~\mu \text{F}\) capacitor and \(40~\Omega\) resistor is connected to \(230~\text{V}\) variable frequency AC source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be:
1. | \(46~\text{rad/s}~\text{and}~54~\text{rad/s}\) |
2. | \(42~\text{rad/s}~\text{and}~58~\text{rad/s}\) |
3. | \(25~\text{rad/s}~\text{and}~75~\text{rad/s}\) |
4. | \(50~\text{rad/s}~\text{and}~25~\text{rad/s}\) |
1. | \( \theta=\sin ^{-1}\left(\dfrac{\pi^2 {R}}{{gT}^2}\right)^{1/2}\) | 2. | \(\theta=\sin ^{-1}\left(\dfrac{2 {gT}^2}{\pi^2 {R}}\right)^{1 / 2}\) |
3. | \(\theta=\cos ^{-1}\left(\dfrac{{gT}^2}{\pi^2 {R}}\right)^{1 / 2}\) | 4. | \(\theta=\cos ^{-1}\left(\dfrac{\pi^2 {R}}{{gT}^2}\right)^{1 / 2}\) |