QAIPMT-2006-Ph-2462: NEET 2006 Physics - Class 11 AIPMT-2006-Ph-2462 Solution: A rectangular block of mass m and area of cross-section A…

Let l be the length of block immersed in liquid as shown in the figure. When the block is floating, _ mg = Al _ m If the block is given vertical displacement y then the effective restoring force is F = _ [ A ( l + y ) _ g _ m g ] = _ [ A ( l + y ) _ g _ A l _ g ] = _ A l _ g y Restoring force = _ [ A l _ g ] y . As this F is directed towards its equilibrium position of block, so if the block is left free, it will execute simple harmonic motion. Here inertia factor = mass of block = m Spring factor = A _ g _ Time period = T = 2 � m A _ g    i.e. T _ 1 A