SOLUTION:The centre of GRAVITY(G) of the wooden BLOCK lies at its midpoint that is at 0.5l from the bottom of the block..Let the block is IMMERSED upto a height 'x', then the centre of buoyancy(B) will be at 0.5x from the bottom of the block.Now the distance between centre of gravity and centre of buoyancy(GB) is 0.5(l - x)From the given,0.5(l - x) = 0.15l ⇒ x = 0.7lNow the immersed height is 0.7lEquating buoyant force and weight,ρb × A × l × g = ρw × A × 0.7l × g\(\Rightarrow \frac {\rho _b }{\rho _w}=0.7\)∴ Specific gravity of wooden block is 0.7 "> SOLUTION:The centre of GRAVITY(G) of the wooden BLOCK lies at its midpoint that is at 0.5l from the bottom of the block..Let the block is IMMERSED upto a height 'x', then the centre of buoyancy(B) will be at 0.5x from the bottom of the block.Now the distance between centre of gravity and centre of buoyancy(GB) is 0.5(l - x)From the given,0.5(l - x) = 0.15l ⇒ x = 0.7lNow the immersed height is 0.7lEquating buoyant force and weight,ρb × A × l × g = ρw × A × 0.7l × g\(\Rightarrow \frac {\rho _b }{\rho _w}=0.7\)∴ Specific gravity of wooden block is 0.7 ">
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A wooden block of length l is made to float in water with its axis vertical. The centre of gravity of the body is 0.15l above the centre of buoyancy. What is the specific gravity of the wooden block?

Fluid Mechanics Buoyancy And Floatation in Fluid Mechanics . 7 months ago

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SOLUTION:The centre of GRAVITY(G) of the wooden BLOCK lies at its midpoint that is at 0.5l from the bottom of the block..Let the block is IMMERSED upto a height 'x', then the centre of buoyancy(B) will be at 0.5x from the bottom of the block.Now the distance between centre of gravity and centre of buoyancy(GB) is 0.5(l - x)From the given,0.5(l - x) = 0.15l ⇒ x = 0.7lNow the immersed height is 0.7lEquating buoyant force and weight,ρb × A × l × g = ρw × A × 0.7l × g\(\Rightarrow \frac {\rho _b }{\rho _w}=0.7\)∴ Specific gravity of wooden block is 0.7
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Posted on 07 Nov 2024, this text provides information on Fluid Mechanics related to Buoyancy And Floatation in Fluid Mechanics. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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