Answer:
(a) 
(b)
Explanation:
It is given that,
Force acting on the particle, F = 12 N
Displacement of the particle, 
Magnitude of displacement, 
(a) If the change in the kinetic energy of the particle is +30 J. The work done by the particle is given by :

is the angle between force and the displacement
According to work energy theorem, the charge in kinetic energy of the particle is equal to the work done.
So,



(b) If the change in the kinetic energy of the particle is (-30) J. The work done by the particle is given by :


Hence, this is the required solution.
Answer:
(a) The initial speed required is 13116 m/s
(b) The escape speed is 10394 m/s
This problem involves the application of newtons laws of gravitation. The forces in action here are conservative and as a result mechanical energy is conserved.
The full calculation can be found in the attachment below.
Explanation:
In both parts (a) and (b) the energy conservation equation were used. Assumption was made that when the object is very far from the planet the distance from the planet's center approaches infinity and the gravitational potential energy approaches zero.
The calculation can be found below.
Answer:
N = 2000 drops approx with 1 cm diameter each
Explanation:
Let the diameter of one drop is 1 cm
so volume of one drop is given by

now we have


now in 1L of liquid let say N drops are there
so we have

now we have


so it will have approx 2000 drops in it with diameter 1 cm each drop
Answer:
0.04455 Hz
Explanation:
Parameters given:
Wavelength, λ = 6.5km = 6500m
Distance travelled by the wave, x = 8830km = 8830000m
Time taken, t = 8.47hours = 8.47 * 3600 = 30492 secs
First, we find the speed of the wave:
Speed, v = distance/time = x/t
v = 8830000/30492 = 289.58 m/s
Frequency, f, is given as velocity divided by wavelength:
f = v/λ
f = 289.58/6500
f = 0.04455 Hz
Answer:

Explanation:
The gravitational force between the proton and the electron is given by

where
G is the gravitational constant
is the proton mass
is the electron mass
r = 3 m is the distance between the proton and the electron
Substituting numbers into the equation,

The electrical force between the proton and the electron is given by

where
k is the Coulomb constant
is the elementary charge (charge of the proton and of the electron)
r = 3 m is the distance between the proton and the electron
Substituting numbers into the equation,

So, the ratio of the electrical force to the gravitational force is

So, we see that the electrical force is much larger than the gravitational force.