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Q. No.A block is suspended from a spring and causes an extension of \(2\) cm. It is now imparted a kinetic energy \(E\) so that the block rises up by exactly \(2\) cm. If the block were to be given the same kinetic energy upward, without being attached to a spring, it would rise up by:
1. \(1\) cm
2. \(2\) cm
3. \(4\) cm
4. \(8\) cm
Subtopic: Elastic Potential Energy |
Level 3: 35%-60%
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The pendulum \(OA\) has a length \(L.\) The bob \(A\) is given an initial velocity towards right when it is at its lowest position. Thereafter it moves in a circular path and collides with the hard surface (at \(60^{\circ}\)) losing \(50\%\) of the kinetic energy it had just before the collision. The pendulum rebounds and it reaches a height of \(\dfrac{3L}{4}\) above its lowest point \(A\). In the absence of the hard surface, it would have risen to a height of:
| 1. | \(\dfrac{3L}{2}\) | 2. | \(\dfrac{5L}{2}\) |
| 3. | \(2L\) | 4. | \(L\) |
Subtopic: Gravitational Potential Energy |
Level 3: 35%-60%
Hints
A heavy uniform rope of mass \(m\) and total length \(L\) is slowly pulled down from the edge of a horizontal table, which exerts a frictional force on the rope, against its motion. The work done by pulling force is \(W_F\) and the work done against friction is \(W_f-\) both during the same time interval. The entire rope remains taut during its displacement. Then,
| 1. | \(W_F=W_f\) |
| 2. | \(W_F>W_f\) |
| 3. | \(W_F<W_f\) |
| 4. | any of the above may be true depending on the coefficient of friction. |
Subtopic: Concept of Work |
Level 3: 35%-60%
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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 |
Level 3: 35%-60%
Hints
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 |
Level 3: 35%-60%
Hints
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 |
Level 3: 35%-60%
Hints
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 |
Level 3: 35%-60%
Hints
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 |
57%
Level 3: 35%-60%
Hints
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 |
59%
Level 3: 35%-60%
Hints
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 |
60%
Level 2: 60%+
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