# The length of the string of a simple pendulum is measured

Question:

The length of the string of a simple pendulum is measured with a meter scale to be $90.0 \mathrm{~cm}$. The radius of the bob plus the length of the hook is calculated to be $2.13 \mathrm{~cm}$ using measurements with a side calipers. What is the effective length of the pendulum? (The effective length is defined as the distance between the point of suspension and the center of the bob.)

Solution:

Effective Length $=(90.0+2.13) \mathrm{cm}$

In the measurement of the $90.0 \mathrm{~cm}$, there are only two significant digits. Keeping this in mind, we have to consider only two significant digits during addition. So,

Effective Length $=(90.0+2.1) \mathrm{cm}=92.1 \mathrm{~cm}$