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

Options

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

Answer

B

Explanation

Apparent weight of object in water
`w prop (("density of object (sphere"))/("density of water ")`
`w prop (d_(s))/(d_(w))`
As cubical expansion ( Y) of metal is less than water that’s why ratio of density of sphere and water will greater at `50^(@)C` than `0^(@)` C.
`((d_(s))/(d_(w)))_(50^(@)C) gt ((d_(s))/(d_(w)))_(0^(@)C)`
`w_(2)gt w_(1)`