Verified Solution • 2025–26 Session moderate

QAIPMT-2006-Ph-2470: NEET 2006 Physics - Class 11 AIPMT-2006-Ph-2470 Solution: In a radioactive material the activity at time \(t_1\) is…

In a radioactive material the activity at time t1t_1 is R1R_1 and at a later time t2t_2 it is R2R_2. If the decay constant of the material is λ\lambda then R1=R2R_1 = R_2 R1=R2e−λ(t1−t2)R_1 = R_2e^{-\lambda(t_1-t_2)} R1=R2eλ(t1−t2)R_1 = R_2e^{\lambda(t_1-t_2)} R1=R2(t2/t1)R_1 = R_2(t_2/t_1).

Multiple Choice Options

  • A R1=R2R_1 = R_2
  • B R1=R2e−λ(t1−t2)R_1 = R_2 e^{-\lambda(t_1 - t_2)}
  • C R1=R2eλ(t1−t2)R_1 = R_2 e^{\lambda(t_1 - t_2)}
  • D R1=R2(t2t1)R_1 = R_2 \left(\frac{t_2}{t_1}\right)

Step-by-Step Verified Solution

Escape velocity of the body from the surface of earth is v = 2 g R For escape velocity of the body from the platform potential energy + kinetic energy = 0 _ G M m 2 R + 1 2 m v 2 = 0 _ f v e s c a p e = G M R 2 . R = g R = f v From the surface of the earth, v e s c a p e = 2 g R _ f v e s c a p e = v e s c a p e 2 , _ f = 1 2

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