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. \(4.2~\text{kg-m/s}\)
1. \(2.1~\text{kg-m/s}\)
2. \(1.4~\text{kg-m/s}\)
3. \(0~\text{kg-m/s}\)
4. \(4.2~\text{kg-m/s}\)
1. \(2~\text{A}\)
2. \(4~\text{A}\)
3. \(0.2~\text{A}\)
4. \(0.4~\text{A}\)
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. | \(\theta=\cos ^{-1}\left(\dfrac{\pi^2 {R}}{{gT}^2}\right)^{1 / 2}\) |
Three resistors having resistances \(r_1, r_2~\text{and}~r_3\) are connected as shown in the given circuit. The ratio \(\frac{i_3}{i_1}\) of currents in terms of resistances used in the circuit is:
1. \(\frac{r_1}{r_1+r_2}\)
2. \(\frac{r_2}{r_1+r_3}\)
3. \(\frac{r_1}{r_2+r_3}\)
4. \(\frac{r_2}{r_2+r_3}\)
A point object is placed at a distance of \(60~\text{cm}\) from a convex lens of focal length \(30~\text{cm}\). If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of \(40~\text{cm}\) from it, the final image would be formed at a distance of:
| 1. | \(30~\text{cm}\) from the plane mirror, it would be a virtual image. |
| 2. | \(20~\text{cm}\) from the plane mirror, it would be a virtual image. |
| 3. | \(20~\text{cm}\) from the lens, it would be a real image. |
| 4. | \(30~\text{cm}\) from the lens, it would be a real image. |
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