An incompressible liquid is kept in a long conductying cylindrical cantainer, which is closed at its top by an airtight light piston. A cylinder of length 10 cm made of material of density 0.65g//cm^(3) floats with half-length submerged in the liquid as shown in the figure. Air trapped in the cylinder has density 1.30kg//m^(3) On placing extra weight on the piston, pressure of the air in the cylinder is increased to 100 times of the initial pressure.What can you conclude? (because Use Boyle's law of air i.e., P_(1)V_(1)=P_(2)V_(2) at constant temperature)

An incompressible liquid is kept in a long conductying cylindrical c

1.	An incompressible liquid is kept in a long conductying cylindrical cantainer, which is closed at its top by an airtight light piston. A cylinder of length 10 cm made of material of density 0.65g//cm^(3) floats with half-length submerged in the liquid as shown in the figure. Air trapped in the cylinder has density 1.30kg//m^(3) On placing extra weight on the piston, pressure of the air in the cylinder is increased to 100 times of the initial pressure.What can you conclude? (because Use Boyle's law of air i.e., P_(1)V_(1)=P_(2)V_(2) at constant temperature)
Answer» Cylinder moves downwards cylinder moves upwards DISPLACEMENT of the cylinder is 0.55 CM Displacement of the cylinder is 0.6 cm Solution :Determination of DENSITY of liquid (`because` not a WATER) `becauserho_(m)Alg=rho_(a)A((l)/(2))g+rho_(w)A((l)/(2))g` `RARR rho_(m) = (rho_(a))/(2) + (rho_(w))/(2) rArr 0.65 = (0.0013)/(2) + (rho_(l))/(2)` `rArr rho_(l) = 1.2987 gm//c c` Determination of displacement (upwards) `100 rho_(a)x = 99 rho_(a) (5) + rho_(l)x` `rArr 100 xx 0.0013 x - 1.2987 x = 99 xx 0.00135 xx 5` `rArrx = 0.55 cm`