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Mechanics

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22 Jan 2007 12:20:07 IST

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A boat is floating on the surface of a river and the boat contains stones. The stones are then dropped on the river. What will happen to the water level?

a) fall b) rise c) remain unchanged d) can't be predicted

In answering this question I will be thankful if a mathematical approach is provided.

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malay

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Joined: 18 Dec 2006

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22 Jan 2007 12:49:50 IST

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the basic funda is: volume of water displaced=rise if level of water.

volume of water displaced depends upon densityof the object(in fact, relative density between the object and the liquid).

If density is gerater than that of water, volume displaced= volume of liquid.

If density is less than that of water, volume displaced=V*a/b
where,
V=volume of object
a=density of object
b=density of water.

in the first case, volume displaced=V*c/b
{V is volume of boat, c is combined density of booat and stone)

in the second case, volume displaced=V*a/b + v
{v is volume of stones, d is their density)

now v< hence in second case, volume displaced=V*a/b

since a is definitely less than c, volume displaced in first case is greater.

CyBorG

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Joined: 6 Jan 2007

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22 Jan 2007 15:31:48 IST

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When there are stones in boat, the stones displace water whose weight is equal to their weight.But when stones are dropped on the river ,they sink because they displace less water whose weight is less than theirs.Therefore water level falls. OPTION a) is the correct answer and I am 100% sure.I hope this is enough.

Krishna Gopal Singh

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Joined: 29 Dec 2006

Posts: 5153

25 Jan 2007 08:24:08 IST

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I think KAB is right. Right answer is a) only

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