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?

The time period of a simple pendulum is T = 2π√(L/g), which depends only on the length L and acceleration due to gravity g, not on the mass. If the length is increased four times (L' = 4L), then T' = 2π√(4L/g) = 2 × 2π√(L/g) = 2T. The mass doubling has no effect on the time period. Therefore, the ratio T':T = 2:1.