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Q.

A body of mass m is released from a height h on a smooth inclined plane that is shown in the figure. Which of the following can be true about the velocity of the block if it is known that the wedge is fixed ? 

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a

v is highest when the spring comes back to natural position

b

v is highest when it just touches the spring 

c

v is highest when it compresses the spring by some amount

d

v is highest at the maximum compression

answer is B.

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Detailed Solution

When net acceleration reverses its direction then speed will be maximum.
Here, velocity of block is down the plane so Speed will increase if net force on block down the plane i.e mgsinθ must be greater than spring force.
When block crosses position of equilibrium then its speed will be maximum. Because after this, net force will be up the plane and speed will decrease.

At equilibrium net force is zero, so 

mgsinθ=kx

At x=mgsinθk, speed will be maximum. 

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