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CBSE Class 11-science Answered

A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure.The coefficient of friction, between the particle and the rough track equals . The particle isreleased, from rest, from the point P and it comes to rest at a point R. The energies, lost by theball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost whenparticle changes direction from PQ to QR.
Why 2 is used in the above solution ,If it is h then why it is being used there.Since we know that work = force(frictional)*distance but 2 is extra here explain why  ?

Asked by Vineeth K | 05 Apr, 2016, 09:22: AM
answered-by-expert Expert Answer
It is given in the problem that the energy losses in parts PQ and QR are equal.
So, the horizontal distance QR will be same as the distance from origin O to Q.
Hence, after equating the energy losses we get 
begin mathsize 14px style mgh minus μmgcosθ straight h over sinθ equals μmg straight h over tanθ
therefore mgh minus μmgcosθ straight h over sinθ equals μmg hcosθ over sinθ
therefore mgh minus μmgcosθ straight h over sinθ minus μmg hcosθ over sinθ equals 0
therefore mgh minus 2 μmgcosθ straight h over sinθ equals 0 end style
This is how the factor 2 comes.
 
Now, in the second part, we take energy loss only in the part QR. Now, this will be half of the total energy loss
as losses in parts PQ and QR are equal.
So, mgh/2 is taken.
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