A cylindrical block of mass \( M \) and area of cross section \( A \) is floating in a liquid of density \( \rho \) and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is _______.
\( \pi \sqrt{\frac{2M}{\rho A g}} \)
\( 2\pi \sqrt{\frac{M}{\rho A g}} \)
\( 2\pi \sqrt{\frac{\rho A}{M g}} \)
\( \pi \sqrt{\frac{\rho A}{M g}} \)
A spherical liquid drop of radius \( R \) acquires the terminal velocity \( v_1 \) when falls through a gas of viscosity \( \eta \). Now the drop is broken into \( 64 \) identical droplets and each droplet acquires terminal velocity \( v_2 \) falling through the same gas. The ratio of terminal velocities \( \dfrac{v_1}{v_2} \) is ______.
Given below are two statements:Statement I: Pressure of a fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension.In the light of the above statements, choose the correct answer from the options given below
Sixty four rain drops of radius \( 1 \, \text{mm} \) each falling down with a terminal velocity of \( 10 \, \text{cm/s} \) coalesce to form a bigger drop. The terminal velocity of bigger drop is ______ \( \text{cm/s} \)
Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is \( 5 \, \text{cm} \) and the area of cross-sections at A and B are \( 6 \, \text{cm}^{2} \) and \( 3 \, \text{cm}^{2} \) respectively. The rate of flow will be ______________ \( \text{cm}^{3} / \text{s} \). \( \text{(take } g = 10 \, \text{m} / \text{s}^{2} \text{)} \)
A water spray gun is attached to a hose of cross sectional area \( 30 \, \text{cm}^2 \). The gun comprises of \( 10 \) perforations each of cross sectional area of \( 15 \, \text{mm}^2 \). If the water flows in the hose with the speed of \( 50 \, \text{cm/s} \), calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)
When a part of a straight capillary tube is placed vertically in a liquid, the liquid raises upto certain height \( h \). If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by \(1\%\) each, then the height of the liquid in the tube will change by ________ \(\%\).
A tub is filled with water and a wooden cube \( 10 \, \text{cm} \times 10 \, \text{cm} \times 10 \, \text{cm} \) is placed in the water. The wooden cube is found to float on the water with a part of it submerged in water. When a metal coin is placed on the wooden cube, the submerged part is increased by \( 3.87 \, \text{cm} \). The mass of the metal coin is ______ gram. (Take water density as \( 1 \, \text{g}/\text{cm}^3 \) and density of wood as \( 0.4 \, \text{g}/\text{cm}^3 \))
The surface tension of a soap solution is \( 3.5\times 10^{-2} \, \text{N} / \text{m} \). The work required to increase the radius of a soap bubble from \( 1 \, \text{cm} \) to \( 2 \, \text{cm} \) is \( \alpha \times 10^{-6} \, \text{J} \). The value of \( \alpha \) is ______. \( \left( \pi=\dfrac{22}{7} \right) \)
The terminal velocity of a metallic ball of radius \( 6 \, \text{mm} \) in a viscous fluid is \( 20 \, \text{cm/s} \). The terminal velocity of another ball of same material and having radius \( 3 \, \text{mm} \) in the same fluid will be ______ \( \text{cm/s} \).
A small metallic sphere of diameter \( 2 \, \text{mm} \) and density \( 10.5 \, \text{g/cm}^3 \) is dropped in glycerine having viscosity \( 10 \, \text{Poise} \) and density \( 1.5 \, \text{g/cm}^3 \) respectively. The terminal velocity by the sphere is ______ \( \text{cm/s} \). \( (\pi = \frac{22}{7} \text{ and } g = 10 \, \text{m/s}^2) \)
A cylindrical vessel of \( 40 \, \text{cm} \) radius is completely filled with water and its capacity is \( 528 \, \text{dm}^3 \) \( (\text{dm} : \) decimeter\() \). The vessel is placed on a solid block of exactly same height as vessel. If a small hole is made at \( 70 \, \text{cm} \) below the top of water level, the horizontal range of water falling on the ground in the beginning is ______ \( \text{cm} \).
