Q. No.A body of mass \(2~\text{kg}\) begins to move under the influence of time dependent force \(\overrightarrow{{F}}=\left(2 {t} \hat{{i}}+6 {t}^2 \hat{{j}}\right)\text{N}\), where \(\hat{i}\) and \(\hat{j}\) are unit vectors along \(x\) and \(y\text{-axis}\) respectively. The power produced by the force at \(t=2~\text{s}\) is: (in W)
1. \(100\)
2. \(200\)
3. \(300\)
4. \(400\)
1. \(100\)
2. \(200\)
3. \(300\)
4. \(400\)
Subtopic: Power |
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An object of mass \(1000~\text{g}\) experiences a time dependent force \(\overrightarrow{{F}}=\left(2 t \hat{\imath}+3 \mathrm{t}^2 \hat{\jmath}\right) \text{N}.\) The power generated by the force at time \(t\) is:
1. \(\left(2 t^2+3 t^3\right) \text W\)
2. \(\left(2 t^2+18 t^3\right)\text W\)
3. \(\left(2 t^3+3 t^5\right) \text W\)
4. \(\left(3 t^3+5 t^5\right) \text W\)
1. \(\left(2 t^2+3 t^3\right) \text W\)
2. \(\left(2 t^2+18 t^3\right)\text W\)
3. \(\left(2 t^3+3 t^5\right) \text W\)
4. \(\left(3 t^3+5 t^5\right) \text W\)
Subtopic: Power |
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A body of mass \(4 ~\text{kg}\) is placed on a plane at a point \(P\) having coordinate \((3,4)~\text m.\) Under the action of \(\vec{F}=(2 \hat{i}+3 \hat{j})~\text{N},\) it moves to a new point \(Q\) having coordinates \((6,10)~\text m\) in \(4 ~\text{s}.\) The average power and instantaneous power at the end of \(4 ~\text{s}\) are in the ratio of:
1. \(4 :3\)
2. \(6 :13\)
3. \(13 :6\)
4. \(1 :2\)
1. \(4 :3\)
2. \(6 :13\)
3. \(13 :6\)
4. \(1 :2\)
Subtopic: Power |
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A sand dropper drops sand of mass \(m(t) \) on a conveyer belt at a rate proportional to the square root of speed \((v)\) of the belt, i.e.
1. \(P \propto \sqrt{v} \)
2. \(P \propto v \)
3. \(P^2 \propto v^5 \)
4. \({P}^2 \propto {v}^3 \)
1. \(P \propto \sqrt{v} \)
2. \(P \propto v \)
3. \(P^2 \propto v^5 \)
4. \({P}^2 \propto {v}^3 \)
Subtopic: Power |
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The force acting on a particle moving in a straight line is given by:
\(\vec{F}=(6 t^2 \hat{i}-3 t \hat{j})\) and its velocity at any instant is \(\vec{v}=(3 t^2 \hat{i}+6 t \hat{j}).\) Then, the instantaneous power delivered by the force at \( t = 2 ~\text s\) is:
| 1. | \(216 ~\text W\) | 2. | \(108 ~\text W\) |
| 3. | \(0 ~\text W\) | 4. | \(54~\text W\) |
Subtopic: Power |
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A truck is moving from rest with constant power \(P.\) If the displacement of the truck is proportional to \(t^n\) where \(t\) is time, then the value of \(n\) is:
1. \(2\)
2. \(\dfrac{3}{2}\)
3. \(\dfrac{1}{2}\)
4. \(\dfrac{5}{2}\)
1. \(2\)
2. \(\dfrac{3}{2}\)
3. \(\dfrac{1}{2}\)
4. \(\dfrac{5}{2}\)
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 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 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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