A thin strip 10 cm long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5 Nm–1 (see figure). The assembly is kept in a uniform magnetic field of 0.1 T. If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of e is N. If the mass of the strip is 50 grams, its resistance 10Ω and air drag negligible, N will be close to -
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The number of oscillations will be 5000.
Explanation:
Given data:
Length of spring "l" = 10 cm
Spring constant = 0.5 Nm–1
Magnetic field strength = 0.1 T
Mass of strip = 50 Grams
Resistance = 10Ω
Solution:
To = 2π √m/k
= 2π / √10
A = Ao e -t/γ
A = Ao/e , t = γ
t = γ = 2m /b
= 2m / b^2l^2/R
= 10^4 s
Thus the time is 10^4 s.
Now count the number of oscillations.
Number of oscillation t/To = 10^4/ 2π / √10
= 5000
Thus the number of oscillations will be 5000
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