1.

A small thin cylindrical glass beaker having an area of cross section "6 cm"^(2) weighs 10 gwt. If floats vertically in water upto a certain depth with 10 lead shots in it, is 8 cm, how many such lead shots can be added further into it before it sinks.

Answer»

Solution :MASS of a beaker, `m_(1)=10g`
The no. of LEAD shots = 10
The mass of each lead shot = 2 g
`:.` the mass of total lead shots = 20 g
`:.` the total mass of the beaker and the lead shots = 30 g
`:.` the VOLUME of water displaced by the beaker with 10 lead shots in it = `30cm^(3)`
area of cross section of the beaker, `a=6cm^(2)`
total length of the beaker, l = 8 cm
`:.` total volume of the beaker `6xx8=48 cm^(3)`
`:.` volume of the beaker above the water surface `=48-30=18cm^(3)`
if the beaker has to sink in water, the total beaker should be immersed in water.
`rArr18cm^(3)` of water has to be displaced further
`rArr18` gwt FORCE should be further added
`:.` number of lead shots that has to be added further
`(18gwt)/(2gwt)=9`


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