Answer to Question #1665 in Mechanics | Relativity for inah

Question

You need to know the height of a room, but you have no tape measure. You fasten one end of a string to the ceiling of the room, and tie a small rock at the other end so it almost touches the floor. You start this simple pendulum swinging slightly, and measure its period, which is 3.50 seconds. How tall is the room? Answer in meters.

Answer 1

The period and the length of mathematical pendulum are related by the following expression:
T = 2 π √(L/g)
Thus the length is L = T²g/4π² = 3.5²* 9.8 / (4*3.14²) = 3.04 [m]