If \( 1000 \) droplets of water of surface tension \( 0.07 \, \text{N/m} \), having same radius \( 1 \, \text{mm} \) each, combine to from a single drop. In the process the released surface energy is: (Take \( \pi = \frac{22}{7} \))
\( 8.8 \times 10^{-5} \, \text{J} \)
\( 7.92 \times 10^{-4} \, \text{J} \)
\( 9.68 \times 10^{-4} \, \text{J} \)
\( 7.92 \times 10^{-6} \, \text{J} \)
A spherical ball of radius \( 1 \, \text{mm} \) and density \( 10.5 \, \text{g/cc} \) is dropped in glycerin of coefficient of viscosity \( 9.8 \) poise and density \( 1.5 \, \text{g/cc} \). Viscous force on the ball when it attains constant velocity is: \( 3696 \times 10^{-x} \, \text{N} \). The value of \( x \) is: (Given, \( g = 9.8 \, \text{m/s}^2 \) and \( \pi = \frac{22}{7} \))
Given below are two statements:Statement I : Pressure in a reservoir of water is same at all points at the same level of water.Statement II: The pressure applied to enclosed water is transmitted in all directions equally.In the light of the above statements, choose the correct answer from the options given below:
Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.Assertion A : A spherical body of radius \( (5 \pm 0.1) \, \text{mm} \) having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is \( 4\% \).Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.In the light of the above statements, choose the correct answer from the options given below:
A mercury drop of radius \( 10^{-3} \, \text{m} \) is broken into \( 125 \) equal size droplets. Surface tension of mercury is \( 0.45 \, \text{N m}^{-1} \). The gain in surface energy is:
A spherical drop of liquid splits into \( 1000 \) identical spherical drops. If \( u_i \) is the surface energy of the original drop and \( u_f \) is the total surface energy of the resulting drops, the (ignoring evaporation), \( \dfrac{u_f}{u_i} = \left( \dfrac{10}{x} \right) \). Then value of \( x \) is ________.
