Question

Your aim is to measure the total length, Y, of a physical pendulum, which consists of a thin rod and a square block welded to the end of the rod. You need to determine the distance from the upper end of the rod (the pivot) to the center of the block. You measure the length L of the rod and the vertical height of the block, b. Naturally, Y = L + (b / 2). The meter stick is quite worn and hard to read. The edges of the block are rough and chewed up so the block's height is difficult to measure.

Your best estimates are L = 82.7 ± 0.4 cm and b = 8.4 ± 0.4 cm.

Calculate the propagated error in Y. Give your answer in the format 0.## in cm.

Answer 1

Generally, a quantity with error is written as,

Given,

Since b is divided using a natural and since natural number doesn't have any error, only the true quantity gets divides and the error value remains the same.

Given,

And the final result is given by,

So rule two be followed while adding 2 quantities with error is'

When a result involves the sum of two quantities having an error, then the error in the result is equal to the sum of error in individual quantities.

Hence,

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