A particle having charge 10 times that of the electron revolves i

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 Multiple Choice QuestionsMultiple Choice Questions

31.

Two sources of equal emf are connected to an external resistance R. The internal resistances of the two sources are R1 and R2 (R2>R1). If the potential difference across the source having internal resistance R2 is zero, then

  • straight R space equals space fraction numerator straight R subscript 2 space straight x space left parenthesis straight R subscript 1 space plus straight R subscript 2 right parenthesis over denominator left parenthesis straight R subscript 2 minus straight R subscript 1 right parenthesis end fraction
  • R = R2-R1

  • straight R space equals space fraction numerator straight R subscript 1 straight R subscript 2 over denominator left parenthesis straight R subscript 1 plus straight R subscript 2 right parenthesis end fraction
  • straight R space equals space fraction numerator straight R subscript 1 straight R subscript 2 over denominator left parenthesis straight R subscript 1 plus straight R subscript 2 right parenthesis end fraction
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32.

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re, rp, r respectively in a uniform magnetic field B. The relation between re, rp, r is:

  • re < r < rp

  • re > rp =  r

  • re < rp =  r

  • re < rp <  r


33.

A proton moves with a speed of 5.0 x 106 m/s along the x-axis. It enters a region where there is a magnetic field of magnitude 2.0 Tesla directed at an angle of 30° to the
x-axis and lying in the xy-plane. The magnitude of the magnetic force on the proton is

  • 0.8 × 10-13 N

  • 1.6 × 10-13 N

  • 8.0 × 10-13 N

  • 8.01 × 10-13 N


34.

A long straight wire of radius R carries a steady current I0, uniformly distributed throughout the cross-section of the wire. The magnetic field at a radial distance r from the centre of the wire, in the region r > R, is

  • μ0I02πr

  • μ0I02πR

  • μ0I0R22πr

  • μ0I0r22πR


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35.

If the cyclotron oscillator frequency is 16 MHz, then what should be the operating magnetic field for accelerating the proton of mass 1.67 x 10-27 kg ?

  • 0.334 πT

  • 3.34 πT

  • 33.4 πT

  • 334 πT


36.

If a magnet is dropped through a vertical hollow copper tube, then

  • the time taken to reach the ground is longer than the time taken, if the tube was made out of plastic

  • the magnet will get attracted and stick to the copper tube

  • the time taken to reach the ground is longer than the time taken, if the tube was made out of stainless steel

  • the time taken to reach the ground does not depend on the radius of the copper tube


37.

Consider a circular wire loop of radius R spinning about a diametrical chord which is perpendicular to uniform magnetic field B0k^

  • The magnitude of the induced EMF in the loop is maximum when the plane of the loop is perpendicular to B

  • Flux through the loop is maximum when the plane of the loop is perpendicular to B

  • The direction of induced current remains same during the spinning motion of the loop

  • EMF induced will be the same for a larger radius of the loop in the same field


38.

A galvanometer of resistance G is converted into an ammeter using a shunt of resistance R. If the ratio of the heat dissipated through the galvanometer and shunt is 3 : 4, then R equals

  • 43 G

  • 34 G

  • 169 G

  • 916 G


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39.

The wire of length l is bent into a circular loop of a single turn and is suspended in a magnetic field of induction B. When a current I is passed. through the loop, the maximum torque experienced by it is

  • 14π BIl2

  • 14π BI2l

  • 14π BIl

  • 14π B2Il


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40.

A particle having charge 10 times that of the electron revolves in a circular path of radius 0.4 m with an angular speed of one rotation per second. The magnetic induction produced at the centre of the circular path is

  • 4π × 10-26 T

  • 2π × 10-26 T

  • 16π × 10-26 T

  • 8π × 10-25 T


D.

8π × 10-25 T

Given,  q = 10 e

Radius, r = 0.4 m

   W = 2π n = 2π × 1       W = 2π        e = 1.6 × 10-19 C

The magnetic induction produced at the centre of the coil

         B = μ0I2rμ0 = 4π × 10-7 MKS units  B = 4π × 10-7 × 10e2 × 0.4 × 1         l = qt = 10e1     = 4π × 10-7 × 10 × 1.6 × 10-190.8     = 8π × 10-25 T


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