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The upper half an inclined plane of inclination 30 is perfectly smooth while the lower half rough. A block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and the lower half of the plane is given by

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a

0.5

b

3

c

23

d

32

answer is C.

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Detailed Solution

v2-u2=2 gsin θL2 for the upper part v2=gsinθ L SINCE u=0 for the lower part 0 -v2=2 gsinθ-μkcosθL2 g sinθL=-gsinθ-μkcosθL SO μK=2 tanθ=23

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The upper half an inclined plane of inclination 30 is perfectly smooth while the lower half rough. A block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and the lower half of the plane is given by