Q

Asked by araima2001 | 9th Sep, 2016, 11:03: AM

Expert Answer:

begin mathsize 12px style Volume space of space the space cone equals 1 third πr squared straight h
Mass space of space the space cone equals straight m subscript 1 equals straight rho cross times 1 third πr squared straight h
Given space that space both space are space made space of space same space material.
Mass space of space the space cylinder equals straight m subscript 2 equals straight rho cross times πr squared straight h
We space know space that
straight Y subscript CM equals fraction numerator straight m subscript 2 straight y subscript 2 plus straight m subscript 1 straight y subscript 1 over denominator straight y subscript 2 plus straight y subscript 1 end fraction
space space space space space space equals fraction numerator straight rho cross times πr squared straight h cross times open parentheses negative begin display style straight h over 2 end style close parentheses plus straight rho cross times 1 third πr squared straight h cross times open parentheses begin display style straight h over 4 end style close parentheses over denominator ρπr squared straight h plus straight rho 1 third πr squared straight h end fraction
space space space space space space equals fraction numerator ρπr squared straight h open parentheses negative begin display style straight h over 2 end style plus 1 third cross times straight h over 4 close parentheses over denominator ρπr squared straight h open parentheses 1 plus 1 third close parentheses end fraction equals fraction numerator open parentheses negative begin display style straight h over 2 end style plus 1 third cross times straight h over 4 close parentheses over denominator open parentheses 1 plus 1 third close parentheses end fraction
space space space space space space equals fraction numerator open parentheses negative begin display style straight h over 2 end style plus begin display style straight h over 12 end style close parentheses over denominator open parentheses 4 over 3 close parentheses end fraction
space space space space space space equals fraction numerator open parentheses begin display style fraction numerator 5 straight h over denominator 12 end fraction end style close parentheses over denominator open parentheses 4 over 3 close parentheses end fraction
straight Y subscript CM equals open parentheses fraction numerator 5 straight h over denominator 16 end fraction close parentheses end style

Answered by Yashvanti Jain | 9th Sep, 2016, 03:13: PM