SHMHard
Question
The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is t0 in air. Neglecting frictional force of water and given that the density of the bob is (4/3) × 1000 kg/m3. What relationship between t and t0 is true :-
Options
A.t = t0
B.t = t0/2
C.t = 2t0
D.t = 4t0
Solution
∵ to = 2π
Effective weight of bob inside water,
W′ = mg - thrust = Vρg vρ′g
Vρgeff = V(ρ - ρ′)g,
where, ρ = Density of bob
⇒ geff =
g and ρ′ = Density of water
∴ t = 2π
= 2π
∴
[∵ ρ′ = 103kg/m3, ρ =
× 103kg/m3]
=
⇒ t = 2t0
Effective weight of bob inside water,
W′ = mg - thrust = Vρg vρ′g
Vρgeff = V(ρ - ρ′)g,
where, ρ = Density of bob
⇒ geff =
g and ρ′ = Density of water∴ t = 2π
= 2π∴
[∵ ρ′ = 103kg/m3, ρ =
× 103kg/m3]=
⇒ t = 2t0Create a free account to view solution
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