Question

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The densities of two metals are 6.3 g/cm³ and 3.7 g/cm³ respectively. The two metals
are of equal mass, and are melted to form an alloy.

What is the new density of the alloy?
A) 4.0 g/cm³ B) 4.7 g/cm³
C) 5.0 g/cm³
D) 10.0 g/cm³

Answer 1

Concept-

• Density = Total Mass / Total Volume

Solution:-

• let d1 and d2 be their respective densities
• d1= 6.3 gram/cm³ , d2 = 3.7 gram/cm³
• let us consider taking m mass of both substance as it is given masses are equal
• Let their volumes be V1 and V2

Now ,

☯︎Density= Total Mass / Total Volume

➪
`density = (m + m)/(V1 + V2)`

➪
`(2m)/( (m)/(d1) + (m)/(d2) )`

`\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (Volume=(mass)/(density))`

➪
`\frac{2\cancel{m}}{ \cancel{m}((1)/(d1) + (1)/(d2)) }`

➪
`(2)/( (1)/(d1) + (1)/(d2) )`

➪
`(2.d1.d2)/( d1+d2 )`

Putting Values -

✰
`(2* 6.3* 3.7)/( 6.3+3.7 )`

➪
`(46.62)/( 10)`

➪
`4.662`

≈
`4.7 gram/cm^3`