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Q. No.A force \(F=F_0+\frac12kx\) (where \(x\) is the rightward displacement of the block \(A\)) acts on the block \(A\) as shown in the figure. The spring is initially unextended and the block is at rest. There is no friction anywhere. The maximum extension in the spring is:
1.
\(\dfrac{F_0}{k}\)
2.
\(\dfrac{2F_0}{k}\)
3.
\(\dfrac{4F_0}{k}\)
4.
\(\dfrac{F_0}{2k}\)
Subtopic: Potential Energy: Relation with Force |
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Air flows past a windmill at a constant speed \(v,\) the area swept by the blades being \(A.\) Assume that the windmill extracts a constant fraction of the energy of the air that flows past it. The power generated by the windmill varies with \(v\) as:
1. \(v^{-1}\)
2. \(v^{1}\)
3. \(v^{2}\)
4. \(v^{3}\)
1. \(v^{-1}\)
2. \(v^{1}\)
3. \(v^{2}\)
4. \(v^{3}\)
Subtopic: Power |
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A particle (mass: \(0.5~\text{kg}\)) moves along a straight line under the action of forces, and its velocity (\(v\)) varies with position (\(x\)) as shown in the figure:
The power delivered to the particle by all the forces acting on it, when it is at \(x=1~\text{m}\), is:
1. \(4~\text{W}\)
2. \(-4~\text{W}\)
3. \(2~\text{W}\)
4. \(-2~\text{W}\)
The power delivered to the particle by all the forces acting on it, when it is at \(x=1~\text{m}\), is:
1. \(4~\text{W}\)
2. \(-4~\text{W}\)
3. \(2~\text{W}\)
4. \(-2~\text{W}\)
Subtopic: Power |
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A particle of mass \(m\) moves in three dimensions with a velocity \(\vec{v}\) and an acceleration \(\vec{a}\) (not necessarily constant). The dot product \(\vec {a}\cdot \vec{v}\) is proportional to:
| 1. | work done by all forces |
| 2. | work done by centripetal forces |
| 3. | power due to all forces |
| 4. | power due to centripetal forces |
Subtopic: Power |
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A constant additional force acts on a body thrown vertically upward under the earth's gravity, the force always opposing the motion. The magnitude of work done by the force during the upward motion is \(W_1\) and during the downward motion is \(W_2.\) Then,
| 1. | \(W_1>W_2\) |
| 2. | \(W_1<W_2\) |
| 3. | \(W_1=W_2\) |
| 4. | Any of the above may be true depending on the initial speed of the body |
Subtopic: Work done by constant force |
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A car is driven by an engine that delivers constant power (except possibly at the initial instant). If it starts from rest, its displacement varies with time \((t)\) as:
1. \(t\)
2. \(\sqrt t \)
3. \(\dfrac{1}{\sqrt t}\)
4. \(t\sqrt t \)
1. \(t\)
2. \(\sqrt t \)
3. \(\dfrac{1}{\sqrt t}\)
4. \(t\sqrt t \)
Subtopic: Power |
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A block of mass \(m\) is slid slowly up a smooth incline \(AB\) and then, its is slowly slid down a second smooth incline \(BC\) until it reaches the ground. Let the magnitude of work done by the person sliding the block be \(W_1\) for the upward path \((AB)\) and \(W_2\) for the downward path \((BC).\) Then,
1. \(W_1=W_2\)
2. \(W_1\text{cos}30^\circ=W_2\text{cos}60^\circ\)
3. \(W\text{sin}30^\circ=W_2\text{sin}60^\circ\)
4. \(W_1\text{tan}30^\circ=W_2\text{tan}60^\circ\)
1. \(W_1=W_2\)
2. \(W_1\text{cos}30^\circ=W_2\text{cos}60^\circ\)
3. \(W\text{sin}30^\circ=W_2\text{sin}60^\circ\)
4. \(W_1\text{tan}30^\circ=W_2\text{tan}60^\circ\)
Subtopic: Work done by constant force |
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Given below are two statements:
| Statement I: | The magnitude of the momentum of a body is directly proportional to its kinetic energy. |
| Statement II: | Kinetic energy increases whenever an external force acts on a moving body. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Concept of Work |
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One end of the vertical spring is fixed to the ground, while the other end is connected to a ring of mass \(m,\) that can slide on a fixed smooth horizontal rod. The ring is given a velocity \(v\) so that it moves to the right up to a distance \(h,\) the length of spring in its initial unextended position. The speed \(v\) equals:
| 1. | \(\sqrt{\dfrac{kh^2}{m}} \) | 2. | \(\sqrt{\dfrac{k(\sqrt2-1)h^2}{m}} \) |
| 3. | \((\sqrt2+1)\sqrt{\dfrac{kh^2}{m}} \) | 4. | \((\sqrt2-1)\sqrt{\dfrac{kh^2}{m}}\) |
Subtopic: Elastic Potential Energy |
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A man of mass \(M\) throws a ball of mass \(m\) vertically upward. At the beginning of the throw, he holds the ball at rest, and releases it at height \(h\) above at the end of it. The ball travels up to a maximum height \(H\) above the point of release. The work done by the man on the ball is \(W_1\) and that done by gravity on the ball is of magnitude \(W_2.\) Both \(W_1\) and \(W_2\) are the work done during the entire motion — from when the man begins the throw, till the ball reaches its maximum height. Then:
| 1. | \(\dfrac{W_1}{W_2}=\dfrac mM\) | 2. | \(\dfrac{W_1}{W_2}=\dfrac hH\) |
| 3. | \(\dfrac{W_1}{W_2}=\dfrac{h}{h+H}\) | 4. | \(\dfrac{W_1}{W_2}=\dfrac 11\) |
Subtopic: Work done by constant force |
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