1
JEE Main 2014 (Offline)
+4
-1
On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius $$R$$ and making a circular contact of radius $$r$$ with the bottom $$R$$ and making a circular contact of radius $$r$$ with the bottom of the vessel. If $$r < < R$$ and the surface tension of water is $$T,$$ value of $$r$$ just before bubbles detach is: (density of water is $${\rho _w}$$) A
$${R^2}\sqrt {{{{\rho _w}g} \over {3T}}}$$
B
$${R^2}\sqrt {{{{\rho _w}g} \over {6T}}}$$
C
$${R^2}\sqrt {{{{\rho _w}g} \over {T}}}$$
D
$${R^2}\sqrt {{{{2\rho _w}g} \over {3T}}}$$
2
JEE Main 2014 (Offline)
+4
-1
There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $${d_1}$$ and $${d_2}$$ are filled in the tube. Each liquid subtends $${90^ \circ }$$ angle at center. Radius joining their interface makes an angle $$\alpha$$ with vertical. Radio $${{{d_1}} \over {{d_2}}}$$ is : A
$${{1 + \sin \,\alpha } \over {1 - \sin \,\alpha }}$$
B
$${{1 + \cos \,\alpha } \over {1 - \cos \,\alpha }}$$
C
$${{1 + \tan \,\alpha } \over {1 - \tan \,\alpha }}$$
D
$${{1 + \sin \,\alpha } \over {1 - \cos \,\alpha }}$$
3
JEE Main 2013 (Offline)
+4
-1
A uniform cylinder of length $$L$$ and mass $$M$$ having cross-sectional area $$A$$ is suspended, with its length vertical, from a fixed point by a mass-less spring such that it is half submerged in a liquid of density $$\sigma$$ at equilibrium position. The extension $${x_0}$$ of the spring when it is in equilibrium is:
A
$${{Mg} \over k}$$
B
$${{Mg} \over k}\left( {1 - {{LA\sigma } \over M}} \right)$$
C
$${{Mg} \over k}\left( {1 - {{LA\sigma } \over {2M}}} \right)$$
D
$${{Mg} \over k}\left( {1 + {{LA\sigma } \over M}} \right)$$
4
AIEEE 2012
+4
-1
A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $$1.5 \times {10^{ - 2}}\,\,N$$ (see figure). The length of the slider is $$30$$ $$cm$$ and its weight negligible. The surface tension of the liquid film is A
$$0.0125\,\,N{m^{ - 1}}$$
B
$$0.1\,\,N{m^{ - 1}}$$
C
$$0.05\,\,N{m^{ - 1}}$$
D
$$0.025\,\,N{m^{ - 1}}$$
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