A small sphere of density \(\rho\) is completely submerged in a liquid of density \(3\rho\) and released. The magnitude of its acceleration just after release equals:
1. \(g\)
2. \(\frac g3\)
3. \(2g\)
4. \(3g\)
Subtopic:  Archimedes' Principle |
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A wooden block with a coin placed on its top, floats in water as shown in the figure.

    

The distances \(\mathrm{l}\) and \(\mathrm{h}\) are shown in the figure. After some time, the coin falls
into the water. Then,

(a) \(\mathrm{l}\) decreases
(b) \(\mathrm{h}\) decreases
(c) \(\mathrm{l}\) increases
(d) \(\mathrm{h}\) increases

Choose the correct alterative/s:

1. (b), (c)
2. (a), (d)
3. (c), (d)
4. (a), (b)

Subtopic:  Archimedes' Principle |
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Two non-mixing liquids of densities \(\rho\) and \(n\rho\) \((n>1)\) are put in a container. The height of each liquid is \(h.\) A solid cylinder of length \(L\) and density \(d\) is put in this container. The cylinder floats with its axis vertical and length \(rL~(r<1))\) in the denser liquid. The density \(d\) is equal to:
1. \([2+(n+1)r ]\rho\)
2. \([2+(n-1)r] \rho\)
3. \([1+(n-1)r] \rho\)
4. \([1+(n+1)r ]\rho\)

Subtopic:  Archimedes' Principle |
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