An asteroid, whose mass is 3.6 × 10-4 times the mass of earth, revolves in a circular orbit around the sun at a distance that is 1.6 times the earth's distance from the sun. (a) calculate the period of revolution of the asteroid in years. (b) what is the ratio of the kinetic energy of the asteroid to the kinetic energy of earth?

a) 2.02 years

b) 8.1 x 10⁻⁸.

Explanation:

Time period of a rotating body T² is proportional to radius of orbit R³ So

T₁² / T₂² = R₁³ /R₂³ ( T₁ and R₁ is time period and radius of orbit of the earth .)

1² / T₂² =( 1/1.6)³

T₂ = 2.02 years.

Kinetic energy of an orbiting body = 1/2 m v₀² ( v₀ is orbital speed)

= 1/2 m x 2 g R = m x G m/R² X R= m² x G /R

Kinetic energy of asteroid K₁ / kinetic energy of earth K₂ =

(mass of asteroid/mass of earth)² x( radius of earth / radius of asteroid)

=( 3.6 x 10⁻⁴)² x 1/1.6 = 8.1 x 10⁻⁸ .

the electric field is a “force field” around a charged object that illustrates the direction the electric force would push an imaginary 

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.