Answer is option A
Kinetic Energy=1/2mv^2
where v is the velocity of the body at any instant.
Now, using the equation of motion,
v^2=2ax
where x is the distance covered and a is the resultant acceleration of the object down the plane.
clearly, KE has linear dependence with x
so the graph of KE vs. Distance covered has to be a straight line.
Now, PE of the object=mgh where h is the height of the object.
we know that, h is proportional to the distance of the object from the ground
ie h=k(l-x) where l is the total length of the plane while x is the distance covered
k is a constant
so PE=kmg(l-x)
KE=max
so PE is a line with negative slope while KE is a line with positive slope
Now,
as half of the PE is lost in heat,sound,etc. the value of KE has to be less than the max. value of the PE[its initial value when the object was on top] when the object reaches the ground.
hence, A is the most appropriate option.
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Last edited by Akshay; Jun 16th 2009 at 02:00 PM.
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