A hollow sphere filled with water is used as the bob of a pendulum. Assume that the equation for the simple pendulum is valid with the distance between the point of suspension and center of mass of the bob acting as the effective length of the pendulum. If water slowly leaks out of the bob, how will the time period vary?
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Answer ⇒ Time period will increases.
Explanation ⇒ Using the Formula,
T = 2π √[m/ρgA(Sinθ₁ + Sinθ₂)],
where m is the mass of the liquid, ρ is the density of fluid, θ₁ and θ₂ are the angle which the object makes with the ground. It is mostly 90°.
or simply, T = 2π√(l/g)
where l is the effective length of the water column + length of the thread from which it is stretched.
Now, if there will be some hole, then water starts leeking. As a result, effective length of water column will decrease. But effective length of the system will increase, as the space occupied by the water will washed.
∴ Time Period will also increase as it is directly proportional to length of the column.
Hope it helps .
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