A body of mass $$0.5$$ kg travels in a straight line with velocity $$v=ax^{3/2}$$ where $$a=5~\mathrm{m^{-1/2}s^{-1}}$$. The work done by the net force during its displacement from $$x=0$$ m to $$x=2$$ m is:
1. $$15$$ J
2. $$50$$ J
3. $$10$$ J
4. $$100$$ J

Subtopic: Â Work Done by Variable Force |
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A horizontal force $$F$$ acts on a $$2$$ kg block placed on a smooth horizontal plane. It varies with time $$t$$ as shown in the figure. The block is initially at rest.

The work done by the force until $$t=2$$ s, equals:
1. $$6.25$$ J
2. $$4.5$$ J
3. $$2.25$$ J
4. $$1.5$$ J
Subtopic: Â Work Done by Variable Force |
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The work done by a force  $$F=2x^2$$ (newton) in a displacement from $$x=0$$ (origin) to $$x=3$$ m is:
1. $$54$$ J
2. $$27$$ J
3. $$18$$ J
4. $$9$$ J
Subtopic: Â Work Done by Variable Force |
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A block is moved along a horizontal plane by means of a force of constant magnitude of $$5$$ N, but acting at an angle $$\theta$$ which is proportional to the displacement ($$x$$):    $$\theta=\frac{1}{2} x,$$
where $$x$$ is in $$\text{m}$$ and $$\theta$$ is in radians. The work done by this force until the force becomes vertical is:

1. $$5$$ J
2. $$10$$ J
3. $$2.5$$ J
4. $$1.25$$ J
Subtopic: Â Work Done by Variable Force |
From NCERT
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A block of mass $$m$$ moving with a speed $$v$$ meets an unextended spring fixed at one end, and having a spring constant $$k.$$ During maximum compression, the mid-point of the spring undergoes a rightward displacement $$x$$. Then, $$v=$$
1. $$\sqrt{\frac{k}{m}}x$$
2. $$\sqrt{\frac{m}{k}}x$$
3. $$\sqrt{\frac{k}{m}}(2x)$$
4. $$\sqrt{\frac{k}{m}}\Big(\frac{x}{2}\Big)$$