Question

The length and width of a living room is 5.5 m and 4.8 m with an uncertainty of 0.1 m in each measurement. The perimeter of the room with associated uncertainty using either the "general method" or the "high/low method" presented in the pre-lab notes is:

(A) 20.6 + 0.2 m
(B) 20.6 0.1 m
(C) 20.6 + 0.6 m
(D) 20.6+ 0.4 m
(E) 20.6t0.8 m

Answer 1

The perimeter of room is
`(20.6 \pm 0.4)~m`

Explanation:

We are given the following in the question:

The length and width of a room are measured with uncertainties.

There is uncertainty of 0.1 m in each measurement.

Length =
`(5.5 \pm 0.1)~m`

Width =
`(4.8 \pm 0.1)~m`

Formula:

The perimeter of room is given by:

`P = 2* (\text{Length + Width})\\P = 2* ((5.5\pm 0.1)+ (4.8\pm 0.1))\\= 2* (10.3\pm 0.2)\\P = (20.6 \pm 0.4)~m`

The uncertainties are also added and multiplied.

Thus,the perimeter of room is
`(20.6 \pm 0.4)~m`