SHMHard
Question
A test tube of length l and area of cross-section A has some iron fillings of mass M as shown in figure. The test tube floats normally in a liquid of density ρ with length x dipped in the liquid. A disturbing force makes the tube oscillate in the liquid. The time period of oscillation is given by -
Options
A.
B.
C.
D.
Solution
at equilibrium position
Axρg = Mg M = Axρ ----------(1)
If tube displaced by distance y vertically downward then net force on tube
A(x + y)ρg − Mg = Ma
a =
y ⇒ a = (g/x)y
Time period T = 2π
Axρg = Mg M = Axρ ----------(1)
If tube displaced by distance y vertically downward then net force on tube
A(x + y)ρg − Mg = Ma
a =
y ⇒ a = (g/x)yTime period T = 2π
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