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A metal ball immersed in alcohol weights...

A metal ball immersed in alcohol weights `W_1` at `0^@C` and `W_2` at `50^@C`. The coefficient of expansion of cubical the metal is less than that of the alcohol. Assuming that the density of the metal is large compared to that of alcohol, it can be shown that

A

`W_(1)gtW_(2)`

B

`W_(1)=W_(2)`

C

`W_(1)gtW_(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`W_(1)=mg-Vd_(a)g`
`W_(2)=mg-V^(')d_(a)^(')g`
`=mg-V(1+50gamma_(b))(d_(a)g)/((1+50gamma))`
`=mg-Vd_(a)g[(1+50gamma_(b))/(1+50gamma_(a))]`
`V=` volume of ball at `0^(@)C`
`d_(a)=` density of alcohool at `0^@C`
`V'=` volume of ball at `50^@C`
`d_(a)^'=`density of alcohol at `0^@C`
Given `gamma_(b)ltgamm_(a)`
`:. 1+50gamma_(b)lt1+50gamma_(a)`
`:.(1+50gamma_(b))/(1+50gamma_(b))lt1`
`:. W_(2)gtW_(1)` or `W_(1)gtW_(2)`
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Knowledge Check

  • A metal ball immersed in alcohol weighs w_(1) " and" 0^(@)C " and" w_(2) " at " 59^(@)C . The coefficient of cubical expansion of the metal is less than that of alcohol. Assuming that the density of the metal is large compared to that of alcohol, it can be shown that

    A
    `w_(1) gt w_(2)`
    B
    `w_(1)=w_(2)`
    C
    `w_(1) lt w_(2)`
    D
    `w_(1)=(w_(1)//2)`

  • A metal ball immersed in water weighs w_(1) at 0^(@)C and w_(2) at 50^(@)C . The coefficient of cubical expansion of metal is less than that of water. Then

    A
    `w_(1)gtw_(2)`
    B
    `w_(1)ltw_(2)`
    C
    `w_(1)=w_(?)`
    D
    Data is insufficient

  • A metal ball immersed in water weighs w_(1) at 5^(@)C and w_(2) at 50^(@)C . The coefficient of cubical expansion of metal is less than that of water. Then

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