Question

A cylindrical block of wood of mass M is floating n water with its axis vertica. It is depressed a little and then released. Show that the motion of the block is simple harmonic and find its frequency.

Answer 1

Answer:

PHYSICS

A cylindrical block of wood of mass m, radius r & density p is floating in water with its axis vertical. It is depressed a little and then released. If the motion of the block is simple harmonic. Find its frequency.

A .

2π1mπr2pg

B .

2π1mπr3pg

C .

4π1mπr2pg

D .

4π1mπr3pg

December 26, 2019Afeera Dhurwey

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ANSWER

Suppose a height h of the block is dipped in the water in equilibrium position. If r be the radius of the cylindrical block, the volume of the water displaced =πr2h. For floating in equilibrium, 

πr2hpg=W .........(i)

where p is the density of water and W the weight of the block. Now suppose during the vertical motion, the block is further dipped through a distance x at some instant. The volume of the displaced water is πr2(h+x) pg vertically upward.

Net force on the block at displacement x from the equilibrium position is 

F=W−πr2(h+x)pg=W−πr2hpg−πr2pxg

Using (i) F=πr