Chapter 13: Q. 14 (page 353)

Planet Z is $10, 000 k m$ in diameter. The free-fall acceleration on Planet Z is role="math" localid="1648089747827" $8.0 m / s^{2} .$
(a) What is the mass of Planet Z?
(b) What is the free-fall acceleration $10, 000 k m$ above Planet Z’s north pole?

Short Answer

Expert verified

(a) The mass of planet Z is $1.25 \times 10^{25} k g .$

(b) The free-fall acceleration $10000 k m$ above Planet Z’s north pole is $2 m / s^{2} .$

Step by step solution

Given information (a)

Diameter of the planet = $10000 k m$ , free-fall acceleration = $8 m / s^{2} .$

Calculation (a)

The formula for free-fall acceleration is given by : $g = \frac{G M}{R^{2}} .$

Substituting the given values, in equation :

role="math" localid="1648091089811"

\Rightarrow (8.0 m / s^{2}) = \frac{(6.67 \times 10^{- 11} N \cdot m^{2} / {kg}^{2}) M}{{(1.0 \times 10^{7} m)}^{2}} . \Rightarrow M = \frac{(8.0 m / s^{2}) {(1.0 \times 10^{7} m)}^{2}}{(6.67 \times 10^{- 11} N \cdot m^{2} / {kg}^{2})} = 1.2 \times 10^{25} kg .

Final answer (a)

The mass of planet Z is $1.25 \times 10^{25} k g .$

Given information (b)

Height from the north pole $h = 10000 km .$

Calculation (b)

The formula for free-fall acceleration at a height h is given by : $g^{'} = \frac{G M}{(R + h)^{2}} .$

Height given in this case is $h = R$ , hence $h = R$ is substituted to the above equation :

$g^{'} = \frac{G M}{(R + R)^{2}} = \frac{G M}{4 R^{2}} = \frac{1}{4} \frac{G M}{R^{2}} = \frac{1}{4} g = \frac{1}{4} (8.0 m / s^{2}) = 2.0 m / s^{2} .$

Final answer (b)

The free-fall acceleration $10000 k m$ above Planet Z’s north pole is $2 m / s^{2} .$

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Planet Z is $10, 000 k m$ in diameter. The free-fall acceleration on Planet Z is role="math" localid="1648089747827" $8.0 m / s^{2} .$
(a) What is the mass of Planet Z?
(b) What is the free-fall acceleration $10, 000 k m$ above Planet Z’s north pole?

Short Answer

Step by step solution

Given information (a)

Calculation (a)

Final answer (a)

Given information (b)

Calculation (b)

Final answer (b)

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Planet Z is 10,000kmin diameter. The free-fall acceleration on Planet Z is role="math" localid="1648089747827" 8.0m/s2.(a) What is the mass of Planet Z?(b) What is the free-fall acceleration10,000kmabove Planet Z’s north pole?

Short Answer

Step by step solution

Given information (a)

Calculation (a)

Final answer (a)

Given information (b)

Calculation (b)

Final answer (b)

One App. One Place for Learning.

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Planet Z is $10, 000 k m$ in diameter. The free-fall acceleration on Planet Z is role="math" localid="1648089747827" $8.0 m / s^{2} .$
(a) What is the mass of Planet Z?
(b) What is the free-fall acceleration $10, 000 k m$ above Planet Z’s north pole?