CBSE Class 12-science Answered
Figure shows the two charged spheres connected to string each of length 20 cm and suspended vertically.
Due to electrostatic repulsive force , strings are diverged and angle between the string is 60o .
(mg) is weight of sphere and T is tension force acting along each string.
Tension force is resolved into two components , (i) vertical component ( T cos30 ) is balanced by weight
and (ii) horizontal component T sin30 is balanced by elctrostatic force Fe /
Hence we get
Fe = T sin30 .....................(1)
mg = T cos30 ....................(2)
By dividing eqn.(1) by eqn.(2) , we get
Fe / ( m g ) = tan30 ..................(3)
Electrostatic force between spheres is
where K = 1/(4πεo) = 9 × 109 N m2 C-2 is Coulomb's constant, q is charge on each sphere and
d is distance beteem spheres . Distance d between spheres is 20 cm because
strings of equal length and line between two spheres makes equilateral triangle .
Hence , mass m is calculated from eqn.(3) as
( mass is very high compare to the answer . It is 4 times the value given in answer .
Hence value of either charge or string length given in the question is not correct )
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When the spheres are immersed in kerosene , then weight of sphere (mg) is replaced by (m -mk) g due to
buoyancy force . Where mk is displaced mass of kerosene Hence ( m- mk ) is determined as explained above .
when spheres are immersed in kerosene , dielectric constant εr = 2 is to be considered in electrostatic force
where d is now , d = 2 × L cos63 , where L is length of string because divergence between strings is reduced to 54o .
If (m-mk) is calculated , we can calculate the value of mk , i.e displaced mass of kerosene.
From the known density of kerosene , we get the displaced volume of kerosene that is equal to volume of sphere .
By knowing mass and volume of sphere , density of material is calculated .