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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

\ F50ºCF0ºC\frac{F_{50ºC}}{F_{0ºC}}=V50ºCV0ºC\frac{V_{50ºC}}{V_{0ºC}}.(ρw)50ºC(ρw)0ºC\frac{(\rho_{w})_{50ºC}}{(\rho_{w})_{0ºC}}=(1+γmΔθ)(1+γwΔθ)\frac{(1 + \gamma_{m}\Delta\theta)}{(1 + \gamma_{w}\Delta\theta)} (Dq = 500 C)

Given that gm < gw \ F50ŗC < F0ŗC

or apparent weight at 500 C will be more.