State whether upthrust will increase or decrease if the density of a liquid in which the solid floats decreases.

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Solution

When an object is partially or wholly immersed in a fluid, an upward thrust acts on it.
This upward thrust is directly proportional to the density of fluid, i.e., more the density of fluid, more is the upthrust and vice versa.
Upthrust by a liquid on an object is calculated as -
$U p t h r u s t = V o l u m e o f t h e o b j e c t \times d e n s i t y o f t h e l i q u i d \times g r a v i t a t i o n a l a c c e l e r a t i o n$
Hence, if the density of the liquid decreases then the upthrust also decreases.

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\begin{matrix} (A) If density of the liquid decreases, x will & (P) Increase (B) If height of the cube is increased keeping base area and density same, x will & (Q) Decrease (C) If the whole system is accelerated upward, then x will & (R) Remain same (D) If the cube is replaced by another cube of same size but lesser density, x will & (S) either increase or decrease \end{matrix}

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