If linear charge density of a wire as shown in the figure is `lambda`

Answer

A-P;B-R;C-SD-Q

Explanation

(A) Buoyant force = Mg = constant `=V_(sub)=(Mg)/(rho_(l)g)` . Volume of displace fluid = constant `therefore` density of fluid must be constant.
(B) `(V_("solid")-V_("sub"))="constant"rArr(V_("solid")-(M_("solid"))/(rho_("liquid")))="constant"Vxx3alphaxxDeltaT=(MgammaDeltaT)/(d)rArr3alpha(d)/(rho)`
(C ) `Ah_("in")d_("lquid")=A(h_("in")
+h_("out"))rho_("solid")=M`(mass of soild)
`h_("out")=-(M)/(Arho_("soild")),h_("in")=(M)/(Arho_("soild"))-(M)/(Ad_("liquid"))=`constant
`(M(1+3alphaDeltaT))/(A(1+2alphaDeltaT)rho)-(M(1+gammaDeltaT))/(A(1+2alphaDeltaT)d)=(M)/(Arho)-(M)/(Ad),gamma=2alpha+alpha(d)/(rho)`
(D) `Ah_("in")d_("liquid")g=` Buoyant force = constant = Mg
`A_(0)(1+2alphaDeltaT)h_("in ")(d)/(1+gammaDeltaT)"constant",h_("in")=(M)/(A_(0)d)(1+(gamma-2alpha)DeltaT)gamma=2alpha`