Decay Problem 4

Classical Mechanics Level 2

A substance decays at the rate of 1% per second. 1 kg of the substance is dropped from a height of 500m. What will be the amount of substance when it falls on the floor? (g=10m/s)

900 g 904 g 907 g 891 g

Archit Boobna by Archit Boobna , 20, India

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2 solutions

Raj Magesh
Sep 28, 2014

Since the substance decays at 1% per second, its rate of change of mass is:

d m d t = − 0.01 m \dfrac{dm}{dt}=-0.01m

Rearranging,

d m m = − 0.01 d t \dfrac{dm}{m}=-0.01 dt

Integrating from t = 0 t=0 to t = 10 t=10 , since the particle takes 10 seconds to hit the floor,

∫ 1 m d m m = − 0.01 ∫ 1 10 d t \int_{1}^{m} \dfrac{dm}{m} = -0.01\int_{1}^{10} dt

ln ⁡ m = − 0.1 \ln{m} = -0.1

m = e − 0.1 ≈ 0.904 k g m=e^{-0.1} \approx \boxed{0.904 kg}

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Nice way of Solving, loved it...

Nafees Zakir - 6 years, 7 months ago
Farhabi Mojib
Oct 14, 2014

We know for compound interest,
A = P ( 1 + r ) n A = P(1+r)^{n}
Taking,
P=1000 g
r = -1% or - 1 100 \frac{1}{100}
and n = 10 s


It comes,
A = 904.38
Rounding this,
904 \boxed{904}

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