A uniform soda can of mass 0.140 kg is 12.0 cm tall and filled with 0.354 kg of soda (Fig. 9-41). Then small holes are drilled in the top and bottom (with negligi- ble loss of metal) to drain the soda. What is the height h of the com of the can and contents a. initially
b. after the can loses all the soda?
c. What happens to h as the soda drains out?
d. If x is the height of the remaining soda at any given instant, find x when the com reaches its lowest point .

Explanation:

a ) The centre of mass of a can filled completely with any liquid of any mass lies at the center of the can or at height h /2 where h is height of the can . So centre of mass of can of mass .140 kg of height 12 cm will lie at height 6 cm . Similarly center of mass of its content will also lie at height 6 cm that is center  point of the content .

Hence overall center of mass of can along with its content will lie at height 6 cm initially  .

b )

After the can loses all the soda , can becomes empty . Hence its center of mass will lie at its center again  .

c ) Its center of mass remains unchanged as the soda drains out completely .

d ) When soda starts draining out of the can , its lower part becomes heavier than the upper part . Hence its center of mass moves downwards . Its height is lowered . As height of soda is lowered in the can , center of mass also is lowered . It reaches its lowest point when soda in the can reaches half the height or when the can is half filled .

After that center of mass again starts rising upwards until the can is completely empty .

the temperature in kelvin of 2.0 dm3 of an ideal gas is doubled and its pressure is increased by a factor of four. what is the final volume of the gas