The length of a simple pendulum is increased four times to its previous value while the mass is doubled. What is the ratio of the new and previous time period of the pendulum?
2:1
Pendulum Time Period Ratio
Given: A simple pendulum's length is increased four times, and its mass is doubled.
Time period of a simple pendulum:
T = 2π √(L / g)
Note: Mass does not affect the time period, so we only consider the length.
Previous time period:
T₁ = 2π √(L / g)
New time period (length = 4L):
T₂ = 2π √(4L / g) = 2π × 2 √(L / g) = 2 T₁
Therefore, the ratio T₂ : T₁ = 2 : 1
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