Q. No.A particle moves unidirectionally on a horizontal plane, under a constant power-supplying energy source. The displacement-time \((s\text-t)\) graph that describes the motion of the particle is:
(graphs are drawn schematically and are not to scale)
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Power |
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A body of mass \(2\text{ kg}\) is driven by an engine delivering constant power \(1~\text{J/s}. \) The body starts from rest and moves in a straight line. After \(9\text{ s}, \) the kinetic energy of the body is:
1. \(4.5~\text{J}\)
2. \(9~\text{J}\)
3. \(13.5~\text{J}\)
4. \(18~\text{J}\)
Subtopic: Power |
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A particle of mass \(m\) is moving in a circular path of constant radius \(r\) such that its centripetal acceleration (\(a\)) is varying with time \(t\) as \(a=k^2rt^2\) where \(k\) is a constant. The power delivered to the particle by the force acting on it is given as:
1. zero
2. \( {m k^2} {r^2} t^2 \)
3. \({mk}^2 {r}^2 {t} \)
4. \({mk}^2 {rt}\)
1. zero
2. \( {m k^2} {r^2} t^2 \)
3. \({mk}^2 {r}^2 {t} \)
4. \({mk}^2 {rt}\)
Subtopic: Power |
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Sand is being dropped from a stationary dropper at a rate of \(0.5\) kgs–1 on a conveyor belt moving with a velocity of \(5\) ms–1. The power needed to keep the belt moving with the same velocity will be:
1. \(1.25\) W
2. \(2.5\) W
3. \(6.25\) W
4. \(12.5\) W
1. \(1.25\) W
2. \(2.5\) W
3. \(6.25\) W
4. \(12.5\) W
Subtopic: Power |
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A particle of mass \(m\) is moving under a force whose delivered power \(P\) is constant. The initial velocity of the particle is zero. The position of a particle at \(t=4\) s is:
| 1. | \(\dfrac{16}{3}\sqrt{\dfrac{2P}{m}}\) | 2. | \(\dfrac{4}{3}\sqrt{\dfrac{2P}{m}}\) |
| 3. | \(\dfrac{2}{3}\sqrt{\dfrac{P}{m}}\) | 4. | \(\dfrac{3}{10}\sqrt{\dfrac{P}{m}}\) |
Subtopic: Power |
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A lift with a mass of \(1400\) kg moves upwards at a constant velocity of \(3\) m/s, and experiences a frictional force of \(2000\) N. What is the power of the motor driving the lift? (take \(g=10\) m/s2)
1. \(48\) kW
2. \(24\) kW
3. \(32\) kW
4. \(42\) kW
1. \(48\) kW
2. \(24\) kW
3. \(32\) kW
4. \(42\) kW
Subtopic: Power |
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How much power is delivered by a force, \(F\) at \(t=10~\text{s}\) (see figure), assuming the body starts from rest?
(take \(g=10\) m/s2)
(take \(g=10\) m/s2)
| 1. | \(50\) W | 2. | \(30\) W |
| 3. | \(20\) W | 4. | \(10\) W |
Subtopic: Power |
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A \(60~\text{HP}\) electric motor lifts an elevator having a maximum total load capacity of \(2000~\text{kg}.\) If the frictional force on the elevator is \(4000~\text N,\) the speed of the elevator at full load is close to:
\(\left(1~ \mathrm{HP}=746 \mathrm{~W}, ~{g}=10 \mathrm{~ms}^{-2}\right) \)
1. \(1.5 \mathrm{~ms}^{-1}\)
2. \(2.0 \mathrm{~ms}^{-1}\)
3. \(1.7 \mathrm{~m} / \mathrm{s}^{-1}\)
4. \(1.9 \mathrm{~m} / \mathrm{s}^{-1}\)
\(\left(1~ \mathrm{HP}=746 \mathrm{~W}, ~{g}=10 \mathrm{~ms}^{-2}\right) \)
1. \(1.5 \mathrm{~ms}^{-1}\)
2. \(2.0 \mathrm{~ms}^{-1}\)
3. \(1.7 \mathrm{~m} / \mathrm{s}^{-1}\)
4. \(1.9 \mathrm{~m} / \mathrm{s}^{-1}\)
Subtopic: Power |
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An automobile of mass \('m'\) accelerates starting from the origin and initially at rest, while the engine supplies constant power \(P.\) The position is given as a function of time by:
1. \(\left(\dfrac{8p}{9m}\right)^{\frac{1}{2}} t ^{\frac{3}{2}}\)
2. \(\left(\dfrac{9p}{8m}\right)^{\frac{1}{2}}t^{\frac{3}{2}}\)
3. \(\left(\dfrac{9m}{8p}\right)^{\frac{1}{2}}t^{\frac{3}{2}}\)
4. \(\left(\dfrac{8p}{9m}\right)^{\frac{1}{2}}t^{\frac{2}{3}}\)
1. \(\left(\dfrac{8p}{9m}\right)^{\frac{1}{2}} t ^{\frac{3}{2}}\)
2. \(\left(\dfrac{9p}{8m}\right)^{\frac{1}{2}}t^{\frac{3}{2}}\)
3. \(\left(\dfrac{9m}{8p}\right)^{\frac{1}{2}}t^{\frac{3}{2}}\)
4. \(\left(\dfrac{8p}{9m}\right)^{\frac{1}{2}}t^{\frac{2}{3}}\)
Subtopic: Power |
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A body of mass \(1~\text{kg}\) begins to move under the action of a time-dependent force \(\overrightarrow{F}=\left(t \hat{i}+3 t^2 \hat{j}\right) ~\text N,\) where \(\hat{{i}}\) and \(\hat{{j}}\) are the unit vectors along the \(x\) and \(y\text-\)axis. The power developed by the above force, at the time \(t = 2~\text s,\) will be:
1. \(40~\text W\)
2. \(60~\text W\)
3. \(80~\text W\)
4. \(100~\text W\)
1. \(40~\text W\)
2. \(60~\text W\)
3. \(80~\text W\)
4. \(100~\text W\)
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