A spring is attached to a wooden cubical block of edge 5cm and placed in a water conatiner as shown in figure. Calculate the maximum weight to be placed on the block so that it is just immersed in water completely. Density of wood `=700"kg/m"^(3)`, spring constant of spring `=70N//m, g=10m//s^(2)`. Assume that initially spring is in its normal length.

Explanation

Edge of block =5 cm
Density of wood `p_(w)=700 kg//m^(3)`
Speicfic gravity of wood =0.7
Height of block inside of water `=5 xx 0.7 =3.5 cm`
Height of block outside water `=5-3.5=1.5 cm`
W=Maximum weight to be put on the block so that it is just immersed.
V=Volume of displaced water
=Volume of block
`=5 xx 5 xx 5`
`=125cm^(3)`
`=125 xx 10^(-6) m^(3)`
Upward buoyant force =Vpg
`=125 xx10^(-6) xx 1000 xx 10`
=1.25N
Here, p=density of water `=1000 kg//m^(3)`
When weight is put on the block, the spring will be compressed by 1.5 cm
To maintain equilibrium, spring will exert an upward force.
Spring force =kx
k=force constant =70 N/m
`x=1.5 cm=1.5 xx 10^(-2) m`
Spring force `=70 xx 1.5 xx 10^(-2) N`
=1.05 N
Spring force and buoyant force are in upward direction.
Weight of block and additional weight kept on the block act in downward direction.
Total weight of block `=W+w =Vp_(w) g+w`
`=125 xx 10^(-6) xx 700 xx 10+w`
`=0.87 N+w`
1.05+1.25N=0.87+w
w=1.43N