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

Options

A. `W_1gtW_2`
B. `W_1=W_2`
C. `W_1ltW_2`
D. None of these

Answer

C

Explanation

(c)`W_1=mg-Vd_(a)g`
W_2=mg-V'd'_ag=mg-V(1+50gamma_b)(d_ag)/(1+1+50gamma_a)`
`=mg-Vd_ag[(1+50gamma_b)/(1+1+50gamma_a)]`
Given `gamma_bltgamma_a`
`:. 1+50gamma_blt1+50gamma_a :. (1+50gamma_b)/(1+50gamma_a)lt1`
`:. W_2gtW_1 or W_1ltW_2`