A cylindrical object with an outer diameter of 20 cm and a mass of 2 kg floats in water, keeping its axis vertical. If it is slightly depressed and subsequently released, determine the time period of the resulting simple harmonic motion of the object.

Step-by-step solution

When the cylindrical object is depressed by a small distance x , the additional buoyant force acts as the restoring force. F = -( Area ) x g F = -( r^2 g) x Comparing this with the standard equation for simple harmonic motion F = -kx , the effective force constant is: k = r^2 g The time period of oscillation is given by: T = 2 m k = 2 m r^2 g Given values: Mass m = 2 kg Radius r = D 2 = 10 cm = 0.1 m Density of water = 1000 kg/m ^3 Acceleration due to gravity g = 9.8 m/s ^2 Substituting the values into the formula: