By the law of universal gravitation, the gravitational force <em>F</em> between the satellite (mass <em>m</em>) and planet (mass <em>M</em>) is
<em>F</em> = <em>G</em> <em>M</em> <em>m</em> / <em>R </em>²
where
<em>• G</em> = 6.67 × 10⁻¹¹ m³/(kg•s²) is the universal gravitation constant
• <em>R</em> = 2500 km + 5000 km = 7500 km is the distance between the satellite and the center of the planet
Solve for <em>M</em> :
<em>M</em> = <em>F R</em> ² / (<em>G</em> <em>m</em>)
<em>M</em> = ((3 × 10⁴ N) (75 × 10⁵ m)²) / (<em>G</em> (6 × 10³ kg))
<em>M</em> ≈ 2.8 × 10¹⁴ kg
<h2>
Answer: 450 Bq</h2>
Explanation:
This problem can be solved using the Radioactive Half Life Formula:
(1)
Where:
is the final amount of radioisotope (decay rate)
is the initial amount of the radioisotope
is the time elapsed
is the half life of the radioisotope
Knowing this, let's find from (1):
(2)
(3)
Finally:
>>> This is the decay rate of the radioisotope
Note it is in Becquerels (Bq), which is the derived unit approved by the <u>International System of Units</u> for radioactivity
Answer:
9.8m/s^2 down (option C)
Explanation:
The only acceleration acting on this motion case in the acceleration due to gravity: 9.8 m/s^2 in the downwards direction.