# A cylindrical object of outer diameter 10 cm, height 20 cm and density 8000 kg m-3 is supported by a vertical spring and is half dipped in water as shown in figure(13-E6). (a) Find the elongation of the spring in equilibrium condition. (b) 1f the object is slightly depressed and released, find the time period of resulting oscillations of the object. The spring constant =500 N m-1.

Given, diameter of the cylinder, d=10 cm. Therefore, radius, r= 5cm.

Height of the cylinder, h=20 cm.

Density of the cylinder,

Spring constant,

Density of water,

(a)In the equilibrium condition, the weight of the cylinder, is supported by the spring and the buoyant force.

Where V is the volume given by

Solving for x, we get

(b) The driving force,

Now, time period,

(ANS)

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