Difference between torque and work

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Torque and work, while sharing the same units (Newton-Meter and Joule), represent distinct physical concepts. Torque is defined as the product of force and the perpendicular distance from the pivot point, making it a vector quantity. In contrast, work is calculated as the product of force and displacement, classifying it as a scalar quantity. The angular equivalent of work incorporates torque and angular displacement, further illustrating their relationship. Understanding these differences is crucial for applying concepts in physics accurately.
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What is difference between Torque and Work Done if Newton-Meter is Joule?



Torque=Force*Perpendicular distance Work =Force*displacement
 
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The units for torque and work happen to have the same dimensions but torque and work are very different concepts. Work is a scalar and torque is a vector.

The angular equivalent of work = force*displacement is:
work = torque*angular displacement

where angular displacement is measured in radians, which is dimensionless, so the unit for torque must necessarily have the same dimension as the unit for work.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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