Question

The acceleration of the moon just before it strikes the earth in the previous question is
(a) 10 m s−2
(b) 0⋅0027 m s−2
(c) 6⋅4 m s−2
(d) 5⋅0 m s−2

Answer 1

The acceleration of the moon is g' = 6.4 m/s

Option (C) is correct.

Explanation:

Distance of moon form centre of earth =  R + R / 4

Now taking L.C.M it gives:

4R + R / 4 = 5 R/4

g' = gR^2 / (5R/4)^2

g' = 6.4 m/s

Thus the acceleration of the moon is g' = 6.4 m/s

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Answer 2

(c) The moon’s acceleration just before it strikes the earth is 6⋅4 m/s².

Explanation:

Radius of the moon is

$R_m = \frac{R_e}{4}$

$R_m = \frac{6400000}{4}$

$R_m = 1600000 m$

The center of the mass, just before the moon hits the earth surface, will be at a distance of ($R_e + R_m$) from the earth's center.

Just before the moon hits the earth, it's acceleration will be according to the below calculation:

$g' = \frac{GM}{(R_e + R_m)^2 }$

$g' = \frac{10 \times 16 }{25 }$

g' = 6.4 m/s²

Therefore the acceleration of the moon before it strikes the surface of the earth is 6.4 m/s²