Question

Hold a pencil in front of your eye at a position where its blunt end just blocks out the Moon. Make appropriate measurements to estimate the diameter of the Moon, given that the Earth–Moon distance is 3.8 × 105 km. Assume that the pencil has a diameter of about 0.7 cm, and it just blocks out the Moon if it is held about 0.75 m from the eye.Express your answer using two significant figures.

Answer 1

Answer:

$D = 3.6 \times 10^6 m$

Explanation:

Since the diameter of the moon position and the diameter of pencil position are in same line

so the angle made by the rays coming from the sun will be same as the angle made by the pencil lead at eye position

so we will have

$\frac{D}{L} = \frac{d}{x}$

here we have

$D$ = diameter of moon

$d$ = diameter of pencil lead = 0.7 cm

$L = 3.8 \times 10^8 m$

$x = 0.75 m$

so we have

$\frac{0.007}{0.75} = \frac{D}{3.8 \times 10^8}$

$D = 3.6 \times 10^6 m$