Answer:
a)- the density of wood is 333.33 Kg/m³
b)-unstable condition
c)-unstable condition
Explanation:
Given data
wooden cylinder = 0.02m x 0.02m x 0.1m
floating = 1/3 × Length
to find out
density of wood, is it stable condition and wood would float stably in alcohol with density 700 kg/m3
Solution
First we find out density of wood
we know density of water is 1000 kg/m³
and we know wood float 1/3 of length so fraction of density will be
density of wood/ density of water = 1/3
density of wood = 1/3 × density of water
density of wood = 1/3 × 1000 = 333.33 Kg/m³
Now in 2nd part we know for stable condition in partially submerged of body the metacentric height is greater than the centroid of body
we check these condition now,
metacentric height (GM)= I/v
I = ( 0.02 × 0.02³ / 12 )
v = ( 0.02 × 0.02 × 0.1 )
(GM)= I/v = ( 0.02 × 0.02³ / 12 ) / ( 0.02 × 0.02 × 0.1 ) = 0.000333
and we know centroid of body (BM) = 0.05 - 0.033 = 0.017
we know height is 0.1m so G act at 0.05 and B act at (0.1 × 0.3 ) = 0.033
we can see that now metacentric height is less than centroid of body so our body is unstable condition
Now in 3rd part we use alcohol so we calculate ratio of density of wood and density of alcohol i.e. = 333.33 / 700 = 0.48
so now our new G will be 0.05 and B will be (0.1 × 0.48 ) = 0.048
metacentric height (GM)= I/v = ( 0.02 × 0.02³ / 12 ) / ( 0.02 × 0.02 × 0.1 ) = 0.000333
centroid of body (BM) = 0.05 - 0.048 = 0.002
we can see that now metacentric height is less than centroid of body so our body is unstable condition
