Solution:

For a partially immersed block, the effective spring constant is \(k_{eff} = k + \rho_l A g\), leading to \(T_p = 2\pi \sqrt{m/(k + \rho_l A g)}\). For a fully immersed block, \(k_{eff} = k\), so \(T_f = 2\pi \sqrt{m/k}\). Since \(k + \rho_l A g > k\), \(T_p < T_f\). So A is true. The time period of a simple spring-mass system \(T = 2\pi \sqrt{m/k}\) is independent of \(g\). So R is true. However, R does not explain A because the change in period is due to effective spring constant, not general independence from \(g\).