Question

A piece of wood is held under water. the up thrust on it will be

Answer 1

It  depends on the density of the wood . If the density of the wood is greater than the density of water, the upthrust will be less and the wood will sink.if the density of the wood is less than the density of water , the upthrust will be more and hence the wood will float. if the density of wood is same or equal to the density of water, half part of the wood will be in water and the other half on the surface of water , hence weight of the wood and buoyant force cancels out each other.

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Answer 2

upthrust force= volume of wood × density of wood × gravitational force
$\frac{4}{3} \pi {r}^{3} \times rho \times g$