# A vertical spring with a force constant $$k$$ is fixed on a table. A ball of mass $$m$$ at a height $$h$$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $$d$$. The net work done in the process is: 1. $$mg(h+d)+\frac{1}{2}kd^2$$ 2. $$mg(h+d)-\frac{1}{2}kd^2$$ 3. $$mg(h-d)-\frac{1}{2}kd^2$$ 4. $$mg(h-d)+\frac{1}{2}kd^2$$

Subtopic:  Elastic Potential Energy |
64%
From NCERT
AIPMT - 2007
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When an object is shot from the bottom of a long, smooth inclined plane kept at an angle of $$60^\circ$$ with horizontal, it can travel a distance $$x_1$$ along the plane. But when the inclination is decreased to $$30^\circ$$ and the same object is shot with the same velocity, it can travel $$x_2$$ distance. Then $$x_1:x_2$$ will be:
1. $$1:2\sqrt{3}$$
2. $$1:\sqrt{2}$$
3. $$\sqrt{2}:1$$
4. $$1:\sqrt{3}$$

Subtopic:  Conservation of Mechanical Energy |
73%
From NCERT
NEET - 2019
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A force $$F = (20 + 10 y)$$ acts on a particle in the $$y$$-direction where $$F$$ is in Newton and $$y$$ is in meter. Work done by this force to move the particle from $$y =0$$ to $$y =1$$ m is:
1. $$20~\text{J}$$
2. $$30~\text{J}$$
3. $$5~\text{J}$$
4. $$25~\text{J}$$
Subtopic:  Work Done by Variable Force |
75%
From NCERT
NEET - 2019
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Water falls from a height of $$60$$ m at a rate of $$15$$ kg/s to operate a turbine. The losses due to frictional forces are $$10$$% of energy. How much power is generated by the turbine? ($$g=10$$ m/s2)
1. $$8.1$$ kW
2. $$10.2$$ kW
3. $$12.3$$ kW
4. $$7.0$$ kW
Subtopic:  Power |
81%
From NCERT
AIPMT - 2008
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The potential energy of a particle in a force field is $$U=$$$\frac{A}{{r}^{2}}-\frac{B}{r}$ where $$A$$ and $$B$$ are positive constants and $$r$$ is the distance of the particle from the center of the field. For stable equilibrium, the distance of the particle is:

 1 $$\frac{B}{A}$$ 2 $$\frac{B}{2A}$$ 3 $$\frac{2A}{B}$$ 4 $$\frac{A}{B}$$

Subtopic:  Potential Energy: Relation with Force |
77%
From NCERT
AIPMT - 2012
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On a frictionless surface, a block of mass $$M$$ moving at speed $$v$$ collides elastically with another block of the same mass $$M$$ which is initially at rest. After the collision, the first block moves at an angle $$\theta$$ to its initial direction and has a speed $$\frac{v}{3}$$. The second block’s speed after the collision will be:

 1 $$\frac{2\sqrt{2}}{3}v$$ 2 $$\frac{3}{4}v$$ 3 $$\frac{3}{\sqrt{2}}v$$ 4 $$\frac{\sqrt{3}}{2}v$$
Subtopic:  Collisions |
66%
From NCERT
NEET - 2015
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A particle of mass $$m$$ is driven by a machine that delivers a constant power of $$k$$ watts. If the particle starts from rest, the force on the particle at time $$t$$ is:
1. $$\sqrt{\frac{m k}{2}} t^{-1 / 2}$$
2. $$\sqrt{m k} t^{-1 / 2}$$
3. $$\sqrt{2 m k} t^{-1 / 2}$$
4. $$\frac{1}{2} \sqrt{m k} t^{-1 / 2}$$

Subtopic:  Power |
53%
From NCERT
NEET - 2015
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Forces acting on a particle have magnitudes of 14, 7, and 7 N and act in the direction of vectors $$6\hat{i} + 2\hat{j} + 3\hat{k}$$$$3\hat{i} - 2\hat{j} + 6\hat{k}$$$$2\hat{i} - 3\hat{j} - 6\hat{k}$$ respectively. The forces remain constant while the particle is displaced from point A: (2, –1, –3) to B: (5, –1, 1). The coordinates are specified in meters. The work done equal to:

 1 75 J 2 55 J 3 85 J 4 65 J
Subtopic:  Work done by constant force |
From NCERT
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A body of mass m dropped from a height h reaches the ground with a speed of 1.4$\sqrt{\mathrm{gh}}$. The work done by air drag is:

1. –0.2mgh

2. –0.02mgh

3. –0.04mgh

4. mgh

Subtopic:  Work Energy Theorem |
65%
From NCERT
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A chain of length L and mass m is placed upon a smooth surface. The length of BA is (L–b). What will be the velocity of the chain when its end A reaches B?

1. $$\sqrt{\frac{2 g \sin \theta}{L}\left(L^2-b^2\right)}$$
2. $$\sqrt{\frac{g \sin \theta}{2 L}\left(L^2-b^2\right)}$$
3. $$\sqrt{\frac{g \sin \theta}{L}\left(L^2-b^2\right)}$$
4. None of these

Subtopic:  Conservation of Mechanical Energy |
From NCERT
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