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CBSE Class 11-science Answered

13th sum plz
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Asked by lovemaan5500 | 27 Jan, 2019, 07:31: AM
answered-by-expert Expert Answer
Let Im and Is be respectively the moment of inertia of (man+turntable)  and spheres. Let ω be the angula speed of roatation.

kinetic energy = begin mathsize 12px style 1 half I subscript m space omega squared space plus space 2 cross times 1 half I subscript s omega squared space equals space 1 half cross times 1 cross times 100 space plus space 2 cross times 1 half cross times open parentheses 2 cross times 1 squared close parentheses cross times 100 space equals space 250 J end style
when the spheres are brought near to man so that their distances between axis of rotation becomes 0.3 m,
moment of inertia of the whole system changes.

Hence to conserve angular momentum, angular speed of rotation increases
 
final angular speed ωf , when the spheres are at a distance 0.3m from axis is given by
 
 ( Im + 2×Is)×ωi = ( Im + 2×Is')×ωf

where Is' is the moment of inertia of spheres when the spheres are brought near to axis
 
Hence begin mathsize 12px style omega subscript f space equals space omega subscript i cross times fraction numerator open parentheses I subscript m plus 2 I subscript s close parentheses over denominator open parentheses I subscript m plus 2 I subscript s apostrophe close parentheses end fraction space equals space 10 cross times fraction numerator open parentheses 1 plus 2 cross times 2 cross times 1 squared close parentheses over denominator open parentheses 1 plus 2 cross times 2 cross times 0.3 cross times 0.3 close parentheses end fraction almost equal to space 36.8 space r a d divided by s end style
final kinetic energy = begin mathsize 12px style 1 half open parentheses I subscript m space space plus space 2 cross times I subscript s apostrophe close parentheses cross times omega subscript f squared space equals space 1 half cross times open parentheses 1 plus 2 cross times 2 cross times 0.3 cross times 0.3 close parentheses cross times 36.8 cross times 36.8 space almost equal to space 921 space J end style
 
Increase in kinetic energy is compensated by the amount work the man has to do when the whole system is rotating,
  to bring the spheres close to axis of rotation,
Answered by Thiyagarajan K | 27 Jan, 2019, 08:26: AM
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