Water rises in a capillary tube of radius $$r$$ upto a height $$h$$. The mass of water in a capillary is $$m$$. The mass of water that will rise in a capillary of radius $$\frac{r}{4}$$ will be

Two waves $$Y_1=0.25 \sin 316 t$$ and $$Y_2=0.25 \sin 310 t$$ are propagating along the same direction. The number of beats produced per second are

A small metal sphere of mass $$M$$ and density $$d_1$$ when dropped in a jar filled with liquid moves with terminal velocity after sometime. The viscous force acting on the sphere is ($$d_2=$$ density of liquid and $$g=$$ gravitational acceleration)

The capacitance of a parallel plate capacitor with air as medium is $$3 \mu \mathrm{F}$$. With the introduction of a dielectric medium between the plates, the capacitance becomes $$15 \mu \mathrm{F}$$. The permittivity of the medium in $$\mathrm{SI}$$ unit is $$[\varepsilon_0=8.85 \times 10^{-12} \mathrm{SI}$$ unit]