Question
Question: A metal ball immersed in water weighs w<sub>1</sub> at 0<sup>0</sup>C and w<sub>2</sub> at 50<sup>0<...
A metal ball immersed in water weighs w1 at 00C and w2 at 500C. The coefficient of cubical expansion of metal is less than that of water. Then –
A
w1> w2
B
w1< w2
C
w1 = w2
D
Data is insufficient
Answer
w1< w2
Explanation
Solution
Apparent weight (wa)
= actual weight (w) – upthrust (F)
Here, F = Vr wg
(rw = density of water)
i.e., F0ŗC =
V0ŗC(rw) 0ŗCg
and F50ŗC =
V50ŗC(rw)50ŗCg
\ F0ºCF50ºC=V0ºCV50ºC.(ρw)0ºC(ρw)50ºC=(1+γwΔθ)(1+γmΔθ) (Dq = 500 C)
Given that gm < gw \ F50ŗC < F0ŗC
or apparent weight at 500 C will be more.