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Q.

A sphere of mass 2 kg and radius 0.5 m is rolling with an initial speed of  1 ms-1 goes up an inclined plane which make an angle of 300 with the horizontal plane, without slipping. How long will the sphere take to return to the starting point A?
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a

0.57 s

b

0.52s

c

0.60 s

d

0.80 s

answer is C.

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Detailed Solution

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For a solid sphere,  k2R2=25
a=9.8sin301+25 
 a=3.5 m/sec2
Time of ascent is given by
 v=u+at0=1−3.5tt=13.5 s
Time of decent
t=13.5sec.  
Due to symmetry of motion.
Total time, T=23.5=0.57 s

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