Work Energy And Power Question 250

Question: A variable force P is maintained tangent to a frictionless cylindrical surface of radius a as shown in figure. By slowly varying this force, a block of weight W is moved and the spring to which it is stretched from position 1 to position 2. The work done by the force P is

Options:

A) $ W a sin \theta $

B) $ \frac{1}{2} ka^{2} {{\theta }^{2}} $

C) $ Wasin \theta + ka^{2}{{\theta }^{2}} $

D) $ Wasin \theta +\frac{1}{2} ka^{2}{{\theta }^{2}} $

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Answer:

Correct Answer: D

Solution:

[d] $ W= mgh +\frac{1}{2}kx^{2} = mg( asin\theta ) +\frac{1}{2} k{{( a\theta )}^{2}} $

$ =Wa\sin \theta +\frac{1}{2}ka^{2}{{\theta }^{2}} $



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