Final answer:
The initial accelerations of the two particles are found by applying Newton's law of universal gravitation to calculate the mutual gravitational force, and then dividing that force by the respective masses of the particles to determine their individual accelerations.
Step-by-step explanation:
The initial accelerations of the two particles, which have masses of 1 kg and 2 kg and are separated by a distance of 50 m, can be found using Newton's law of universal gravitation. The force of gravity between two masses is given by the equation:
F = G * (m1 * m2) / r^2
Where:
- F is the gravitational force between the masses,
- G is the gravitational constant (6.674 x 10^-11 N(m/kg)^2),
- m1 and m2 are the masses of the two objects,
- r is the separation between the center of the masses.
Once we calculate the force, we can find the acceleration of each mass using Newton's second law:
a = F / m
where:
- a is the acceleration,
- m is the mass of the object being accelerated.
Plugging in the values and solving for each mass will give us the initial accelerations of the particles due to their mutual gravitational attraction.