A metal ball immersed in alcohol 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 the alcohol. Assuming that the density of the metal is large compared to that of alcohol, it can be shown that

Options

A. `W_1 = W_2`
B. `W_1 gt W_2`
C. `W_1 lt W_2`
D. `none of these

Answer

C

Explanation

(c ) As the coefficent of cobical expanison of metal is less as compared to the coefficient of cubical expansion of liquid we may neight the expansion of metal ball. So when the ball is immersed in alcohol at `0^@ C` and has weight `W_1`
`W_1 = W_0 -Wrho_0g`
Where `W_0` = weight of ball in air Similarly, `W_2 = W_0 - V rho_(50)g` Where `rho_g` = density fo alcohol at `0^@C`
As `rho_(50) lt rho_0`,
`:. W_2 gt W_1 or W_1 lt W_2`