If a machine exerts a force of 250 N on an object and no work is done, what must have occurred?
A) The machine has broken
B) The object has not moved
C) The object has gained momentum
D) The object has moved, but then stopped

A prisoner pushes on the prison wall trying to escape. He is unable to get the wall to move. Describe the work done by the prisoner.
A) The prisoner does no work because he applied no force.
B) The prisoner does a lot of work because the wall is heavy
C) The prisoner does work because extends a lot of effort
D) The prisoner does no work because the wall goes no distance

A 3.0-kg cart rolls down a hill. Assume that the height of the cart changes from a maximum of 4.0 meters at the top of the hill to 0.0 meters at the bottom. The speed of the cart changes from 0.0 m/s to 3.0 m/s. How much kinetic energy does the cart have when it is half way down the hill?
A) 6.0J
B) 12.0J
C) 58.8J
D) 117.6J

Explanation:

1) As we know that the work done is the product of force and displacement

It is given as

so if the object is not displaced due to the force exerted by the object then the work done by the object must be ZERO

so correct answer is

B) The object has not moved

2) As we know that the work done is the product of force and displacement

It is given as

As we know that the wall is not displaced due to applied force so here work done by the prisoner must be zero

D) The prisoner does no work because the wall goes no distance

3) As we know by work energy theorem that work done by all forces is equal to change in its kinetic energy

So we will have

so we will have

now when cart moves half the distance then again using the same

probably not if net force is zero

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.