From a uniform circular disc of radius R and mass 9M, a small dis

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 Multiple Choice QuestionsMultiple Choice Questions

11.

Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surface of spheres A and B is

  • 1 : 4

  • 4 : 1

  • 1:2

  • 1:2

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12.

Which of the following units denotes the dimensions ML2 /Q2, where Q denotes the electric charge?

  • Weber (Wb)

  • Henry (H)

  • Wb/m2

  • Wb/m2

182 Views

13.

A charged ball B hangs from a silk thread S which makes an angle θ with a large charged conducting sheet P, as shown in the figure. The surface charge density σ of the sheet is proportional to

  • cos θ

  • cot θ

  • sin θ

  • sin θ

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14.

Two point charges + 8q and – 2q are located at x = 0 and x = L respectively. The location of a point on the x axis at which the net electric field due to these two point charges is zero is

  • 2L

  • L/4

  • 8L

  • 8L

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15.

Two thin wires rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are +q and –q. The potential difference between the centres of the two rings is 

  • QR divided by 4 πε subscript 0 straight d squared
  • fraction numerator straight Q over denominator 2 πε subscript 0 end fraction open square brackets 1 over straight R minus fraction numerator 1 over denominator square root of straight R squared plus straight d squared end root end fraction close square brackets
  • zero

  • zero

174 Views

16.

A charged particle q is shot towards another charged particle Q which is fixed, with a speed v it approaches Q upto a closest distance r and then returns. If q were given a speed 2v, the closest distances of approach would be

  • r

  • 2r

  • r/2

  • r/2

341 Views

17.

Four charges equal to −Q are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium the value of q is

  • negative straight Q over 4 space left parenthesis 1 space space plus 2 square root of 2 right parenthesis
  • straight Q over 4 space left parenthesis 1 space space plus 2 square root of 2 right parenthesis
  • negative straight Q over 2 space left parenthesis 1 space plus 2 square root of 2 right parenthesis
  • negative straight Q over 2 space left parenthesis 1 space plus 2 square root of 2 right parenthesis
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18.

From a uniform circular disc of radius R and mass 9M, a small disc of radius R/3 is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is:

  • 379MR2

  • 4MR2

  • 409MR2

  • 10 MR2


B.

4MR2

let σ be the mass per unit area.

The total mass of the disc = σ x πR2 = 9M
The mass of the circular disc out

 = σ x πR32 = σ x πR29 = M

Let us consider the above system as a complete disc of mass 9M and a negative mass M superimposed on it. Moment of Inertia (I1) of the complete disc (9MR2)/2 about an axis passing through O and perpendicular to the plane of the disc.

M.I. of the cut-out portion about an axis passing through O and perpendicular to the plan of disc

12 x M x R32

Therefore, M.I (I2) of the cut out portion about an axis passing through O and perpendicular to the plane of disc

= 12 x M x R32 + M x 2R32

Using perpendicular axis theorem

Therefore, the total M.I. of the system about an axis passing through O and perpendicular to the plane of the disc is
I = I1 + I2

 = 12 9 MR2 - 12 x M x R32 + M x 2R32 = 9MR22-9MR218 = (9-1) MR22 = 4MR2


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19.

A charge Q placed at the centre of a metallic spherical shell with inner and outer radii R1 and R2 respectively. The normal component of the electric field at any point on the Gaussian surface with radius between R1 and R2 will be

  • Zero

  • Q4πR12

  • Q4πR22

  • Q4π (R1 - R2)2


20.

A sphere of radius R has a uniform volume charge density ρ. The magnitude of electric field at a distance r from the centre of the sphere, where r > R, is

  • ρ4πε0r2

  • ρR2ε0r2

  • ρR3ε0r2

  • ρR33ε0r2


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