IIT JEE , AIEEE Forum - Physics , Mechanics

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A wooden block with base of area A and height 3L is floating on water in a water tank with length L immersed. The block carries n stones each of volume (1/15000) times the volume of the block given.

Density of wood=0.1 gm cc^-1

Densith of stone=5.0 gm cc^-1

Density of water=1.0 gm cc^-1

The height of the tank is H.

The value of n can be:

(a)600 (b)700 (c)800 (d)900

When one among the n stones was dropped into the water,the depth of immersion of the block becomes:

(a)0.999L (b)0.900L (c)0.990L (d)0.909L

The depth of immersion of the wooden block when the block carries (n/2) stones is:

(a)0.650L (b)0.700L (c)0.750L (d)0.800L

karthik2007

Solution:

1. Using archimedes principle, we have:

(3AL)0.1 x g + n/15000 x 3AL x 5 x g = AL

Solving, we get n=700.

2. Again, using archimedes principle, we get:

3ALx0.1xg + (n-1)/1500 x 3AL x 5 x g = Ax (Let the depression be some x)

Or, we get 0.3L + 0.699L = x

or x = 0.999L

3.

Archimedes principle gives:

3Al x 0.1 x g + n/30000 x 3AL x g x 5 = Ax

which gives x = 0.65L on solving.

Feel free to ask any doubts.

rakhiagrawal

@ karthik
plz.provide the formula.

karthik2007

let me try to explain in simple terms:

Go to your bathroom, fill a bucket with water, and try to dip an empty mug in it. You experience an upward force right? As another example, consider a boat, floating in water. Now, the force on the boat is mg downwards. But, if mg is the only force, then how will the boat float?

Hence, we conclude that the liquid exerts an equal and opposite force, in order to support the load. But of course, this has its limits. You cannot make any weight float in water.

Now, archimedes's principle gives us a method of calculating this force.

It simply states that, the force exerted by the liquid on the load is equal to the weight of the liquid displaced, ie, volume of the liquid displaced x density of the liquid (not that of the solid) x g.

Here, in the first question, a length L of the block stays inside water. What does that mean? It simply means that the block must have displaced a length L of water. Hence, volume of water displaced is A x L.
Now, for the block to float, the downward force, ie, the weight of the block + the weight of the stones must be equal to the weight of the liquid displaced (Note that on RHS, we use the density of water/liquid)

Do invest some time in trying out the other parts yourself.

rakhiagrawal

thanks karthik!
yah!i m getting 700 now!but the densities r in cgs system .so we have 2 convert them 2 mks.& 2 get the weight of block,we r taking the density of water & 4 calculation of the weight of stone,the density of stone,i.e .5,right?
m i right?

karthik2007

No need. The units get cancelled on both sides.

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