The acceleration of gravity on the surface of the moon is 1.6 m / s ^ 2.

The acceleration of gravity on the surface of the moon is 1.6 m / s ^ 2. How long should a mathematical pendulum be for its oscillation period on the moon to be 4.9 s?

To find the length of the thread of the mathematical pendulum under consideration, we apply the formula: T = 2 * Π * √ (l / gl), whence we express: l / gl = T ^ 2 / (4 * Π ^ 2) and l = T2 * gl / (4 * Π ^ 2).

Variables and constants: T – period of oscillations on the Moon (T = 4.9 s); gл – acceleration of gravity on the Moon (according to the condition gл = 1.6 m / s2).

Calculation: l = T ^ 2 * gl / (4 * Π ^ 2) = 4.92 * 1.6 / (4 * 3.14 ^ 2) = 0.974 m.

Answer: The thread of the mathematical pendulum under consideration must have a length of 0.974 m.