Answer:
b) tan a = 3
Explanation:
Draw a free body diagram (see attached).
There are three forces acting on the insect. Weight downwards, normal force towards the center of the hemisphere, and friction tangent to the surface.
Sum of the forces in the radial direction:
∑F = ma
N − mg cos α = 0
N = mg cos α
Sum of the forces in the tangential direction:
∑F = ma
μN − mg sin α = 0
Substituting:
μ(mg cos α) − mg sin α = 0
μ cos α − sin α = 0
μ cos α = sin α
μ = tan α
The maximum possible value of the angle is such that its tangent is equal to the coefficient of friction.
Choices 'A', 'C', and 'D' are off-base.
Here are some 'reasons' to put into the mish-mash:
-- third law of motion
-- action and reaction forces
-- conservation of momentum
The relationship between force (F), mass (m) and acceleration (a) is described in the equation F = ma. This equation means that a new force acting on a body will change velocity, and conversely, a change in velocity will generate a force
When parallel rays of light hit a rough or bumpy surface, there will be diffused reflection. Meaning, the light that bounces after it hits a rough or bumpy surface is not parallel anymore and cannot form an image. The answer to this question is 'diffused reflection'.