a
(a)

The weight of lump is given as,

\(W _1= mg\)

The volume of a lump is given as,

\(V =\frac{ m }{\rho_1}\)

The weight of lump in brine solution is given as,

\(W _2= mg -\frac{\rho g V }{2}\)

\(= mg \left(1-\frac{\rho}{2 \rho_1}\right)\)

The new readings of the spring balance is given as,

\(W^{\prime}=m g\left(1-\frac{\rho}{2 p_1}\right)\)

\(=200 \times\left(1-\frac{1.1}{2 \times 11.4}\right)\)

\(=190.35\,gF\)

Thus, the new reading of the spring balance is \(190.35\,gF\).