A small metal sphere of density is dropped from height h into a jar containing liquid of density ( > q ) . The maximum depth up to which the sphere sinks is (Neglect damping forces)

Step-by-step solution

Energy at liquid surface: The sphere enters with kinetic energy KE_s = mgh from conservation of mechanical energy. Forces in liquid: Gravitational force F_g = mg downward, buoyant force F_B = (m/ ) g upward. Work-energy theorem: Net work equals change in kinetic energy from surface to maximum depth x , where final kinetic energy is zero: mgx - (m/ ) gx = -mgh Dividing by mg and solving for x : x(1 - / ) = -h x = -h - = h - Since > , the depth x is positive. Among the options, D has the correct magnitude and variabl