N lamps each of resistance r, are fed by the machine of resistanc

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 Multiple Choice QuestionsMultiple Choice Questions

151.

If the nucleus Al presubscript 13 presuperscript 27 has a nuclear radius of about 3.6 fm, then Te presubscript 52 presuperscript 125 would have its radius approximately as: 

  • 6.0 fm

  • 9.6 fm

  • 12.0 fm

  • 12.0 fm

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152.

Two radioactive substance A and B have decay constants 5λ and λ respectively. At t = 0 they have the same number of nuclei. The ratio of a number of nuclei of A to those of B will be open parentheses 1 over straight e close parentheses squared after a time interval:

  • 1/ 4λ

  • 1/2λ

371 Views

153.

Monochromatic light of frequency 6.0 x 1014 Hz is produced by a laser. The power emitted is 2 x 10-3 W The number of photons emitted, on the average, by the source per second is:

  • 5 x 1015

  • 5 x 106

  • 5 x 1017

  • 5 x 1017

267 Views

154.

The binding energy of deuteron is 2.2 MeV and that of  He presubscript 2 presuperscript 4 is 28 MeV. If two deuterons are fused to form one He presubscript 2 presuperscript 4 then the energy released is

  • 25.8 MeV

  • 23.6 MeV

  • 19.2 MeV

  • 19.2 MeV

352 Views

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155.

In a radioactive material the activity at time t1 is R1 and at a later time t2, it is R2. If the dacay constant of the material is λ, then

  • R1 = R2 e-λ(t1 -t2 )

  • R1 = R2 eλ(t1 -t2 )

  • R1 = R2 e(t2 /t1 )

  • R1 = R2 e(t2 /t1 )

655 Views

156.

The radius of germanium (Ge) nuclide is measured to be twice the radius of Be presubscript 4 presuperscript 9. The number of nucleons in Ge are

  • 73

  • 74

  • 75

  • 75

703 Views

157.

Radioactive material 'A' has a decay constant '8λ' and material 'B' has decay constant 'λ'. Initially, they have a same number of nuclei. After what time, the ratio of a number of nuclei of material 'B' to that 'A' will be 1/e?

  • 1/λ

  • 1/7λ

  • 1/8λ

  • 1/8λ

1640 Views

158.

For a radioactive material, the half-life is 10 minutes. If initially there are 600 number of nuclei, the time is taken (in minutes) for the disintegration of 450 nuclei is

  • 20

  • 10

  • 15

  • 30


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159.

When the radioactive isotope 22688 decays in a series by the emission of three alpha (α) and a beta (β) particle, the isotope X which remains undecay is

  • X21483

  • X21883

  • X22083

  • X22383


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160.

N lamps each of resistance r, are fed by the machine of resistance R. If light emitted by any lamp is proportional to the square of the heat produced, prove that the most efficient way of arranging them is to place them in parallel arcs, each containing n lamps, where n is the integer nearest to.

  • rNR3/2

  • NRr1/2

  • (NRr)3/2

  • (NRr)1/2


B.

NRr1/2

As each is containing n lamps, hence,

The resistance of each arc = nr

Number of arcs = N/n

Total  resistance S is given by

1S = Σ1nr = Nn1nrS = n2rN Total resistance = R + S  + (n2r)N

If E is the emf of the machine, current entering the arcs is E/(R+S) and in each arc is nE/(R+S)N.

Hence, the current passing through each lamp.

I = nEN(R +n2r/N) = ENRn + nrN-1

Now heat produced per second in the lamps is 

H = NI2

since, light emitted is proportional to H2 therefore, the light produced is maximum when H2 and hence H is maximum or Rn + nrN is minimum. Hence, we can write,

Rn + nrN = Rn1/2 - nrN1/2 + 2RrN1/2

This is minimum when R/n - nr/N = 0 or very small or n is closely equal to (NR/r)1/2

 


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