A cork floating in water experiences an upward thrust of 6.3gf. If whole of system falls freely under gravity, then what will be the upward thrust on the cork?

When a body is falling freely it is in the state of weightlessness. Since the upward thrust is equal to weight of the water displaced by cork, which is zero due to free fall, thus upward thrust will be zero.
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Why do we make the bottom of a ship heavy? 


The bottom of a ship is made heavy to keep the centre of gravity of ship below the centre of buoyancy so that the ship is in stable equilibrium.

If the ship gets disturbed from the equilibrium position due to any disturbance in the water medium, the torque produced by weight and buoyant force brings the ship back to equilibrium position. 


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A balloon filled with gas is made to just float on the surface of water. What will happen to it if it is submerged a certain distance below the surface and released?

The weight of the balloon is just balanced by upward thrust on the surface. When it is pushed inside, due to additional pressure of water column, the gas in the balloon gets compressed as a result of which the upward thrust decreases. Now the weight of the balloon is greater than the upward thrust and the balloon will sink as the equilibrium is disturbed.
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An empty balloon weighs 100gm. How much will it weigh if 100gm of air is filled in the balloon at one atmospheric pressure?

Given that an empty balloon weighs 100 g. If this same amount of air is filled in the balloon at one atmospheric pressure, then the same volume of atmosphere will be displaced  as much it is inside the balloon. This increase in weight of the balloon due to weight of air is balanced by the upward thrust. So, the actual weight of the air filled balloon will remain the same, i.e., 100 g.



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A man is sitting in a boat floating in the pond. If the man drinks some water from the pond, then what will happen to the level of water in the pond?

When the man sitting on a boat drinks water, the level of the water tend to decrease as a result of decrease in the volume of water in the pond. As the man gulp down the water, his weight will also increase by mass m. Due to increase in the weight of the man, the boat will sink a little and displace the the same volume of water drank by the man. Hence, the level of water in the pond raised is equal to the level fallen when the man drank the water. 

Thus, the level of water will remain unchanged. 
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