Q24 of 81 Page 273

A wooden block of mass 0.5 kg and density 800 kg m-3 is fastened to the free end of a vertical spring of spring constant 50 N m-1 fixed at the bottom. If the entire system is completely immersed in water find (a) the elongation (for compression) of the spring in equilibrium and (b) the time-period of vertical oscillations of the block when it is slightly depressed and released.

Given, mass of the wooden block,

Density of the block,


Density of water,


Spring constant,


The weight of the block is balanced by the spring and the buoyant force.




Solving for x, we get



(b) The buoyant force and the weight of the block are fixed. Therefore, the only unbalanced force is that due to spring, which will drive the system.



From which, we will get time period, .


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