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Q.

A uniform solid sphere rolls on a horizontal surface at 20 m/s. It then rolls up an incline having an angle of inclination of 30o with the  Horizontal. If the friction losses are negligible, the value of height h above the ground where the ball stops is

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a

14.3 m

b

28.6 m

c

57.2 m

d

9.8 m

answer is B.

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Detailed Solution

Applying the law of conservation of energy, we have12mv2+12Iω2=mghor 12mv2+1225mr2ω2=mghor 12mv2+15mv2=mghh=710×v2g=7×(20)210×9⋅8=28⋅6m
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A uniform solid sphere rolls on a horizontal surface at 20 m/s. It then rolls up an incline having an angle of inclination of 30o with the  Horizontal. If the friction losses are negligible, the value of height h above the ground where the ball stops is