A cubical block of wood of side a and density rho floats in a water of density to rope the lower surface of cube
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Answer:
D
a(a
2
ρg+
2
K
)
In first case, the block just touches the spring i.e. spring has its natural length (no compression)
&
the block of density ρ floats in liquid of density 2ρ, so we have according to law of floatation.
weight of the block= weight of water displaced
a
3
ρg=x×a
2
×2ρg
⇒x=
2
a
i.e. block is half submerged in first case.
in second case, when the block is completely submerged spring is compressed by
2
a
&
block and extra weight W are in rest. i.e Net force is zero
⇒ net downward force = net upward force
⇒ weight of block + extra weight = buoyant force+ spring force
⇒a
3
ρg+W=a
3
×2ρg+K(
2
a
)
W=a
3
ρg+
2
Ka
=a(a
2
ρg+
2
K
)
Explanation:
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