A uniform solid cylinder of density `0.8g//cm^3` floats in equilibrium in a combination of two non-mixing liquids A and B with its axis vertical. The densities of the liquids A and B are `0.7g//cm^3` and `1.2g//cm^3`, respectively. The height of liquid A is `h_A=1.2cm.` The length of the part of the cylinder immersed in liquid B is `h_B=0.8cm`. (a) Find the total force exerted by liquid A on the cylinder. (b) Find h, the length of the part of the cylinder in air. (c) The cylinder is depressed in such a way that its top surface is just below the upper surface of liquid A and is then released. Find the acceleration of the cylinder immediately after it is released.

A uniform solid cylinder of density `0.8g//cm^3` floats in equilibrium

1.	A uniform solid cylinder of density `0.8g//cm^3` floats in equilibrium in a combination of two non-mixing liquids A and B with its axis vertical. The densities of the liquids A and B are `0.7g//cm^3` and `1.2g//cm^3`, respectively. The height of liquid A is `h_A=1.2cm.` The length of the part of the cylinder immersed in liquid B is `h_B=0.8cm`. (a) Find the total force exerted by liquid A on the cylinder. (b) Find h, the length of the part of the cylinder in air. (c) The cylinder is depressed in such a way that its top surface is just below the upper surface of liquid A and is then released. Find the acceleration of the cylinder immediately after it is released.
Answer» Correct Answer - A::B::C (a) As the pressure exerted by liquid A on the cylinder is radial and symmetric, the force due to this pressure cancels out and the net value is zero. (b) For equilibrium, Buoyant force =weight of the body `impliesh_Arho_A Ag+h_Brho_BAg =(h_A+h+h_B)Arho_Cg` (where `rho_C=` density of cylinder) `h=((h_Arho_A+h_Brho_B)/(rho_C))-(h_A+h_B)=0.25cm` (c) `a=(F_(Buoyant-Mg)/(M))` `=[(h_Arho_A+rho_B(h+h_B)-(h+h_A+h_B)rho_C)/(rho_C(h+h_A+h_C))]g` `=g/6` upwards

Discussion

No Comment Found

Related InterviewSolutions

A bubble having surface tension T and radius R is formed on a ring of radius b `(b lt gt R)` . Air is blown inside the tube held in front of the ring , with velocity `upsilon` as shown in fig. The air molecules collides perpendicularly with the wall of the bubble and stops. Calculate the radius R at which the bubble and stops. Calculate the radius R at which the bubble separates from the ring.
A uniform solid cylinder of density `0.8g//cm^3` floats in equilibrium in a combination of two non-mixing liquids A and B with its axis vertical. The densities of the liquids A and B are `0.7g//cm^3` and `1.2g//cm^3`, respectively. The height of liquid A is `h_A=1.2cm.` The length of the part of the cylinder immersed in liquid B is `h_B=0.8cm`. (a) Find the total force exerted by liquid A on the cylinder. (b) Find h, the length of the part of the cylinder in air. (c) The cylinder is depressed in such a way that its top surface is just below the upper surface of liquid A and is then released. Find the acceleration of the cylinder immediately after it is released.
A man is sitting in a boat which is floating in a pond. If the man drinks some water from the pond, the level of water in the pond decreases.
Water in a closed tube (see fig) is heated with one arm vertically placed above a lamp. Water will begin to circulate along the tube in counter-clockwise direction.
A body floats in a liquid contained in a beaker. The whole system as shown in Figure falls freely under gravity. The upthrust on the body is A. (a) zeroB. (b) equal to the weight of the liquid displacedC. (c) equal to the weight of the body in airD. (d) equal to the weight of the immersed portion of the body
A wire fixed at the upper end stretches by length l by applying a force F. The work done in stretching isA. (a) 2FlB. (b) FlC. (c) `(F)/(2l)`D. (d) `(Fl)/(2)`
A homogeneous solid cylinder of length L(LltH/2), cross-sectional area A/5 is immersed such that it floats with its axis vertical at the liquid-liquid interface with length L/4 in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure `P_0`. Then density D of solid is given by A. (a) `5/4d`B. (b) `4/5d`C. (c) `4d`D. (d) `d/5`
A block of ice with a lead shot embedded in it is floating on water contained in a vessel. The temperature of the system is maintained at `0^@C` as the ice melts. When the ice melts completely the level of water in the vessel rises.
A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?A. (a) B. (b) C. (c) D. (d)
Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is T, density of liquid is `rho` and L is its latent heat of vaporization.A. (a) `rhoL//T`B. (b) `sqrt(T//rhoL)`C. (c) `T//rhoL`D. (d) `2T//rhoL`

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment