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Chapter 13: Q. 10 (page 353)

A sensitive gravimeter at a mountain observatory finds that the free-fall acceleration is 0.0075m/s2 less than that at sea level. What is the observatory鈥檚 altitude?

Short Answer

Expert verified

The observatory鈥檚 altitude is2.44km.

Step by step solution

01

Given information.

The free-fall acceleration of observatory is 0.0075m/s2less than that at sea level.

02

Calculation.

Consider the height of the observatory is h.

Hence, the free-fall acceleration on the observatory isg=GM(R+h)2.

So, the difference in the free-fall acceleration is :

螖g=GMR2-GM(R+h)2=GMR2-GMR2[1+hR]2.=GMR2[1-(1+hR)-2].=GMR2[1-1+2hR].

Ignoring higher order term as h鈮�R=2ghR.

Now, rearrange the above equation to get the h,

h=螖gR2g.

Now substitute the values of g, R and 螖gto calculate the

localid="1648481629645" h=(0.0075m/s2)(6.37脳106m)2(9.8m/s2)=2.44脳103m=2.44km.

03

Final answer.

The observatory鈥檚 altitude is2.44km.

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