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A crane is used to lower weight into the sea (sea water density = 1025 kg/m3) for an underwater construction project. What is the percentage reduction in the tension in the rope of the crane due to a rectangular 0.4 m × 0.4 m × 3 m concrete block (density = 2300 kg/m3) when it is completely immersed in water compared to the tension in the rope when it was suspended in air
  • a)
    45%
  • b)
    55%
  • c)
    65%
  • d)
    75%
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A crane is used to lower weight into the sea (sea water density = 102...
When the block is suspended is air [considering negligible buoyant force because of air]
Considering Equilibrium T1 = mg
When the block is completely immersed in water
Where FB = Buoyancy Force because of water
T2 = mg − FB
% reduction in tension = T1 − T2 / T1 × 100
= (mg − mg + FB / mg) × 100
= FB / mg x 1000
= ρseawater × Volume of block / g ρconcrete × Volume of block × g × 100
=
ρseawater / ρconcrete × 100 = 1025 / 2300 × 100 = 44.56%
≃ 45%
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Most Upvoted Answer
A crane is used to lower weight into the sea (sea water density = 102...
To solve this problem, we need to calculate the tension in the rope both when the concrete block is suspended in air and when it is completely immersed in water. Then we can find the percentage reduction in tension.

Given data:
Density of sea water (ρw) = 1025 kg/m3
Density of concrete block (ρc) = 2300 kg/m3
Dimensions of concrete block: length (l) = 3 m, width (w) = 0.4 m, height (h) = 0.4 m

1. Tension in the rope when the concrete block is suspended in air:
To calculate the tension in the rope when the concrete block is suspended in air, we need to consider the weight of the block and the force due to gravity acting on it.
Weight of the block (Wc) = volume of the block × density of the block
= l × w × h × ρc
= 3 × 0.4 × 0.4 × 2300
= 1104 kg

Tension in the rope when the block is suspended in air (Tair) = Wc × g
= 1104 × 9.81
= 10823.04 N

2. Tension in the rope when the concrete block is completely immersed in water:
When the block is immersed in water, there is an additional buoyant force acting on it in the upward direction. This buoyant force is equal to the weight of the water displaced by the block.
Volume of the block (Vc) = l × w × h
= 3 × 0.4 × 0.4
= 0.48 m3

Buoyant force (B) = volume of water displaced × density of water × g
= Vc × ρw × g
= 0.48 × 1025 × 9.81
= 4920.96 N

Tension in the rope when the block is completely immersed in water (Twater) = Wc × g - B
= 10823.04 - 4920.96
= 5902.08 N

3. Percentage reduction in tension:
Percentage reduction in tension = (Tair - Twater) / Tair × 100
= (10823.04 - 5902.08) / 10823.04 × 100
= 4920.96 / 10823.04 × 100
= 45.44%

Therefore, the percentage reduction in tension in the rope due to the completely immersed concrete block is approximately 45%, which corresponds to option A.
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A crane is used to lower weight into the sea (sea water density = 1025 kg/m3) for an underwater construction project. What is the percentage reduction in the tension in the rope of the crane due to a rectangular 0.4 m × 0.4 m × 3 m concrete block (density = 2300 kg/m3) when it is completely immersed in water compared to the tension in the rope when it was suspended in aira) 45%b) 55%c) 65%d) 75%Correct answer is option 'A'. Can you explain this answer?
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