A cylinder of uniform cross-section is immersed into two liquids as shown in Fig. Equal volume of cylinder is submerged in both the liquids and density of cylinder is ρ. The magnitude of acceleration of the cylinder at the shown instant is g/K. Where equal volume of cylinder in two liquids. Find the value of K.
Physics · Mixed Chapter
JEE Mains

Question

A cylinder of uniform cross-section is immersed into two liquids as shown in Fig. Equal volume of cylinder is submerged in both the liquids and density of cylinder is ρ. The magnitude of acceleration of the cylinder at the shown instant is g/K. Where equal volume of cylinder in two liquids. Find the value of K.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The upper liquid has density ρ and the lower liquid has density 2ρ. The submerged volume in each liquid is V/2. Step 2: The upward buoyant force is B=ρg(V/2)+2ρg(V/2)=(3/2)ρVg. Step 3: The cylinder's weight is W=ρVg. Net upward force is B−W=(1/2)ρVg. Step 4: Since cylinder mass is ρV, acceleration a=(B−W)/(ρV)=g/2. Thus g/K=g/2 and K=2.