Question

A cylindrical block of wood when cut through the middle

Answer 1

Answer:

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Step-by-step explanation:

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 =πr

2

h. For floating in equilibrium,

πr

2

hpg=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 πr

2

(h+x) pg vertically upward.

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

F=W−πr

2

(h+x)pg=W−πr

2

hpg−πr

2

pxg

Using (i) F=πr

2

pgx=−kx,

where k = πr

2

pg.

Thus, the bock executes SHM with frequency.

v=

2π

1

m

k

=

2π

1

m

πr

2

pg

.