Question 28

When one moves from a point 16 km below the earth's surface to a point 16 km above the earth's surface. The change in g is approximately $$\alpha$$ %. The value of $$\alpha$$ is _______. (Take radius of the earth = 6400 km.)

Use variation of g:

• above surface:
$$gₕ\approx g(1−2h/R)$$

• below surface:
$$g_d\approx g(1−d/R)$$

given:

h = d = 16 km
R = 6400 km

step 1: values

$$g_{below}=g(1−16/6400)=g(1−1/400)=0.9975g$$

$$g_{above}=g(1−2\times16/6400)=g(1−32/6400)=g(1−1/200)=0.995g$$

step 2: change in g

$$Δg=0.9975g−0.995g=0.0025g$$

step 3: percentage change

$$0.25\%\frac{0.0025g}{g}\times100=0.25\%$$

Create a FREE account and get:

Download resources