disc of moment of inertia 2 x 10 kg m is rotating freely about an
avis through its centre at 60 r.p.m. When a piece of wax is dropped
gently on to the disc 5 cm from the axis, the revolution per minute
dropped to 50. Calculate the mass of the wax. [Ans: 16 x 10 kg]
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Initially
L=Iω
Given that
I=2x10
ω= 60x2π/60 = 2π
So now,
L = 40π
When the wax is dropped on the disc
Revised I = 20 +m (0.05)^2 [where m is the mass of wax]
I = 20 + 0.25m
By conservation of angular momentum
I initial = I final
40π = (20+0.25m) x (50x2π/60)
On solving for m we get
m = 16 kg
L=Iω
Given that
I=2x10
ω= 60x2π/60 = 2π
So now,
L = 40π
When the wax is dropped on the disc
Revised I = 20 +m (0.05)^2 [where m is the mass of wax]
I = 20 + 0.25m
By conservation of angular momentum
I initial = I final
40π = (20+0.25m) x (50x2π/60)
On solving for m we get
m = 16 kg
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