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CBSE Class 9 Answered

An ornament weighing 36 g in air, weighs only 34 g in water. Assuming that some copper is mixed with gold to prepare the ornament, find the amount of copper in it. Specific gravity of gold is 19.3 and that of copper is 8.9

 

Referring to this problem, suppose, the goldsmith argues that he has not mixed copper or any other material with gold, rather some cavities might have been left inside the ornament. Calculate the volume of the cavities left that will allow the weights given in that problem.

Asked by Paresh | 31 Dec, 2015, 12:51: PM
answered-by-expert Expert Answer
begin mathsize 12px style Given colon Weight space of space ornament space in space air comma space straight W subscript air equals 36 space straight g Weight space of space ornament space in space water comma space straight W subscript water equals 34 space straight g Specific space gravity space of space gold comma space straight rho subscript straight g equals 19.3 space straight g divided by cc Specific space gravity space of space copper comma space straight rho subscript straight c equals 8.9 space straight g divided by cc Let space straight v subscript straight c space be space the space volume space of space copper space and space straight v subscript straight g space end subscript be space the space volume space ogold Loss space of space weight equals wight space of space displacement space water space left parenthesis buoyance right parenthesis space equals space 36 minus 34 space equals space 2 space straight g straight W space equals space straight v subscript straight g cross times straight rho subscript straight g cross times straight g plus straight v subscript straight c cross times straight rho subscript straight c cross times straight g space 36 space straight g space equals space 19.3 straight v subscript straight g space cross times space straight g space plus 8.9 straight v subscript straight c cross times straight g space rightwards double arrow straight m subscript straight g plus straight m subscript straight c equals 36 space space space space space space space space left parenthesis 1 right parenthesis N o w comma space left parenthesis V subscript g plus V subscript c right parenthesis straight rho subscript straight w cross times straight g space equals space 2 space cross times space straight g rightwards double arrow open parentheses fraction numerator straight m subscript straight g over denominator space straight rho subscript straight g end fraction plus fraction numerator straight m subscript straight c right parenthesis over denominator space ρc end fraction close parentheses straight rho subscript straight w cross times straight g space equals space 2 space cross times space straight g space rightwards double arrow open parentheses fraction numerator straight m subscript straight g over denominator 19.3 end fraction plus fraction numerator straight m subscript straight c over denominator space 8.9 end fraction close parentheses space equals space 2 space space space space space space left parenthesis 2 right parenthesis Solving space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis mass space of space gold space in space orrnament comma space straight m subscript straight g equals 33.75 mass space of space copper space in space ornament comma space straight m subscript straight c equals 2.225 S i n c e comma space t h e space g o l d s m i t h space a r g u e s space t h a t space h e space h a s space n o t space m i x e d space c o p p e r space o r space a n y space o t h e r space m a t e r i a l space w i t h space g o l d comma space r a t h e r space s o m e space c a v i t i e s space m i g h t space h a v e space b e e n space l e f t space i n s i d e space t h e space o r n a m e n t. N o w comma rightwards double arrow open parentheses fraction numerator straight m subscript straight g over denominator space straight rho subscript straight g end fraction plus V subscript c a v i t y end subscript close parentheses straight rho subscript straight w cross times straight g space equals space 2 space cross times space straight g space rightwards double arrow open parentheses fraction numerator 33.75 over denominator 19.3 end fraction plus V subscript c a v i t y end subscript close parentheses space equals space 2 space space space space rightwards double arrow V subscript c a v i t y end subscript equals 0.251 space end style
Answered by Priyanka Kumbhar | 04 Jan, 2016, 11:06: AM

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