Question

A stone of relative density 'k' is released from rest on the surface of a lake if viscous effects are ignored,
the stone sinks in water with an acceleration is

A Ferry boat has internal volume lmand weight 50kg. Neglecting the thickness of wood the fraction of
volume of the boat immersed in water is,

If a leak develops in the bottom and water starts coming in, The fraction of boats volume will be filled
with water before water starts coming in from the sides is

please answer the question with explanation​

Answer 1

The acceleration with which the stone sinks in the water is a = g ( 1 - 1/k)

Explanation:

Let the mass of the is stone =  M

Volume = V

k = ρ s / ρ  w

Net force acting on the stone F(net) =Mg - F B

Where Fb  is weight of water displaced.

F B =  V ρ  w  g =  Vρs g / k = Mg  / k

F (net) = Mg - Mg / K = Mg ( 1 - 1/k)

a = F (net) /M = Mg /M  ( 1 - 1/k) = g  ( 1 - 1/k)

Thus the acceleration with which the stone sinks in the water is a = g ( 1 - 1/k)

Also learn more

What is the acceleration of a race car that moves at constant velocity of 300 km/h?

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