The loss of weight of a solid when immersed in a liquid at `0^(@)C` is `W_(0)` and at `t^(@)C` is `'W'`. If cubical coefficient of expansion of the solid and the liquid are `gamma_(s)` and `gamma_(1)` then `W =`

Options

A. `W_(0)[bot+(gamma_(s)-gamma_(L))t]`
B. `W_(0)[bot-(gamma_(s)-gamma_(L)t]`
C. `W_(0)[(gamma_(s)-gamma_(L))t]`
D. `W_(0)t//(gamma_(s)-gamma_(L))`

Answer

A

Explanation

Loss in weight = weight of water displaced
`W_(0)=rho_(l_(0))(V_(S_(0))) " so",(W_(0))/(W)=((rhol_(0))/(rho_(l)))((V_(S_(0)))/(V_(s)))`
`W=rho_(1)(V_(s))`
`W=W_(0)(rho_(l))/(rho_(l_(0))).(V_(s))/(V_(s_(0)))`
`W=W_(0)(V_(l_(0)))/(V_(l)).(V_(s))/(s0)=W_(0)[+(l+(gamma_(s)-gamma_(L))t]` using binomial expansion.