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 60^o .

(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 F_e /

Hence we get

F_e = T sin30  .....................(1)

mg = T cos30  ....................(2)

By dividing eqn.(1) by eqn.(2) , we get

F_e / ( m g ) = tan30 ..................(3)

Electrostatic force between spheres is

where K = 1/(4πε_o) = 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 -m_k) g due to

buoyancy force . Where m_k is displaced mass of kerosene Hence ( m- m_k ) is determined as explained above .

when spheres are immersed in kerosene , dielectric constant ε_r = 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 54^o .

If (m-m_k) is calculated , we can calculate the value of m_k , 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 .