Astronauts on the first trip to mars take along a pendulumthat has a period on earth of 1.50 {\rm s}. the period on mars turns out to be 2.45{\rm s}.what is the free-fall acceleration onmars?

3.7 m/s^2

Explanation:

The period of a simple pendulum is given by:

where L is the length of the pendulum and g is the free-fall acceleration on the planet.

Calling L the length of the pendulum, we know that:

is the period of the pendulum on Earth, and is the free-fall acceleration on Earth

is the period of the pendulum on Mars, and is the free-fall acceleration on Mars

Dividing the two expressions we get

And re-arranging it we can find the value of the free-fall acceleration on Mars:

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.