Test: Common Forces in Mechanics

Making the free body diagram of the pendulum bob we get
T.cosθ = mg
T.sinθ = ma (applying the concept of pseudo force)
By dividing the above two equations we get
tanθ = a/g
Thus we get a = g.tanθ
= 10 x tan 5°
= 0.87 ms-2

Normal force is the perpendicular component of the reaction force wrt the surface and thus it always acts perpendicularly to the surface.

For an object at rest to be at rest, no net acceleration must act upon it, which implies no net force. Thus the two forces need to nullify each other, which is only possible if both are equal but opposite.

What do you think about Newton's 1st law, he was said that " every body have nature to maintain inertia of rest or motion untill there is not net force applied on that body". means body will be earlier state (no change in state) when net force applied on that body equals zero.
I know, you thought answer is option (a). but this is not true. for better understanding, Let's take. an example. a body moves with uniform velocity then, net force applied on body = 0 because acceleration of body is zero . but here you see body is not in rest . it is in motion. it is in earlier state . its state doesn't change.

“Every body continues to be in its state of rest or of uniform motion in a straight line unless compelled by an unbalanced external force.” It is simply expressed as if the net external force on a body is zero, its acceleration is zero. Acceleration can be non-zero only if there is a net external force on the body.

In mechanics, if the net external force on the particle is zero, then the particle is said to be in state of equilibrium. By definition.

Action Force and Reaction Force are in opposite directions.
So, the angle between them is 180º

Making the free body diagram of the body we get
T_1.cosθ = T₂ = mg = 60
T_1.sinθ = 50N
By dividing the above two equations we get
tanθ = 5/6
Thus we get θ = 40°

At equilibrium condition net force on body is 0
F1 + F2 = 0
F1 = -F2

The force exerted by the earth on a body is called gravitational force. Actually this force exists between any two bodies in the universe.This force is always of attraction. e.g. When a body is dropped from a height it moves in downward direction towards the Earth with increasing speed (with constant acceleration). This constant acceleration by which all bodies fall down is called acceleration due to gravity. Its value is 9.8 m/s' (approx 10 m/s' )on the surface of the earth. e.g. i) A fruit from tree falls down;ii) Water falls down on a ground from a tap.iii) We feel the weight of bucket full of water holding in our hand. 

In a simple case such as an object resting upon a table, the normal force on the object is equal but in opposite direction to the gravitational force applied on the object (or the weight of the object), that is, , where m is mass, and g is the gravitational field strength (about 9.81 m/s2 on Earth).

Friction is a surface phenomenon. When two surfaces have irregularities that come in contact do they get interlocked  preventing them against sliding each other. So, frictional force is a contact force dependent on the surface.
Gravitational force, electrostatic force and magnetic force does not depend on the surface.

The minimum angle that an inclined plane makes with the horizontal when a body placed on it just begins to slide down is called angle of repose.

A body is said to be in equilibrium only when the net resultant of all external forces applied on the body becomes zero. It does not depend upon any of the internal forces because for any system internal forces exist in pairs because of Newton's third law  and hence they result in null.

The force exerted by a spring is called a restoring force; it always acts to restore the spring toward equilibrium. In Hooke's law, the negative sign on the spring's force means that the force exerted by the spring opposes the spring's displacement.

Concept: Forces.The particle is a stationary under the effect of forces F₁, F₂ and F₃.
This shows that force F₁ is equal and opposite to the resultant of forces F₂ and F₃.
Hence, if the force F₁ is removed the particle will move under the action of the force -ve F₁ and the acceleration will the particle will be,a =-F₁/m.
 

Because the Tension for rope at each point is always the same.

if an object is moving in a horizontal circle at constant speed, the centripetal force does not do any work and cannot alter the total mechanical energy of the object. For the reason, the kinetic energy and therefore the speed of the object will remain constant.

The component of contact force normal to the surfaces in contact is called normal reaction. The component parallel to the surfaces in contact is called friction.