The gravitational field at the Moon in N/kg due to the Earth is approximately (G = 6.67 × 10-11 N m2/kg2, the mass of the Earth is 5.98 × 1024 kg, and the distance to the Moon is 3.85 × 108 m)

F = 2.69 10⁻³ m   [ N]

Explanation:

This exercise asks to calculate the gravitational field of the Earth on the lunar surface, let's use the universal gravitation law

          F = G m M / r²

where m is the mass of the body, M the mass of the Earth and r the distance between the Earth and the Moon

         F = (G M / r²) m

         F = (6.67 10⁻¹¹ 5.98 10²⁴ / (3.85 10⁸)² ) m

         F = 2.69 10⁻³ m   [ N]

This force is directed from the Moon towards the Earth, therefore it reduces the weight of the body

a charge 3q is at the origin, and a charge −2q is on the positive x axis at x=a. part a where on the x-axis would you place a third charge so it would experience no net electric force? enter an expression for the exact answer, which will involve a square-root sign. (do not enter an approximate decimal answer.)

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.