Matric Physics 9th Ch 4 Turning Effect of Forces Ex Questions
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Q 4.2 Define the following:
(i) Resultant vector
(ü) Torque
(iii) Centre of mass
(iv) Centre of gravity
Ans. (i) Resultant Vector: Resultant vector is a single vector that has same effect as the combined effect of all the vectors to be added. This gives the magnitude and direction of the resultant force.
(ii) Torque: The turning effect of a force is called torque.
Torque =τ=FxL
(iii) Centre of Mass: Centre of mass of a system is such a point where an applied force causes the system to move without rotation.
(iv) Centre of Gravity: A point where the whole weight of the body appears to act vertically downward called centre of gravity of body.
Q 4.3 Differentiate the following:
(i) Like and unlike forces
(ii) Torque and couple
(iii)Stable and neutral equilibrium
(i) Like and Unlike forces
Ans. Like forces: Like forces are the forces that are parallel to each other and have the same direction.
Unlike forces:Unlike forces are the forces that are parallel but have directions opposite to each other.
(ii) Torque and Couple
Ans. Torque: The turning effect of a force is called torque or moment of the force.
Torque =τ=FxL
Couple: A couple is formed by two unlike parallel forces of the same magnitude but not acting along the same line.
(iii) Stable and Neutral equilibrium:
Ans. Stable equilibrium: A body is said to the be in stable equilibrium if after a slight tilt it returns to its previous position.
Neutral equilibrium: If a body remains in its new position when disturbed from its previous position, it is said to be in the state of neutral equilibrium. In this state centre of gravity remains at the same position.
Q 4.4 How head to tail rule helps to find the resultant of forces?
Ans. A resultant force is a single force that has the same effect as the combined effect of all the forces to be added.”
One of the method for the addition of forces is a graphical method called head to tail rule method.
Head to tail rule
We will consider the following rules to add forces.
- Select a suitable scale in order to add the forces.
- Draw the vectors of all the forces according to the suitable scale; named as vectors A and B:
- Draw the vector A and then place the vector B such that tail of vector Adding vectors B coincides with the head of the first vector A.
- Now draw a resultant vector R such that its tail is at the tail of Vector A, the first vector, while its head is at the head of vector B, the last vector.
- Vector R represents the resultant force with magnitude and direction.
Q 4.5 How can a force be resolved into its rectangular components?
Ans. “The process of splitting up of a force into two mutually perpendicular components is called the resolution of force”.
Perpendicular components (Rectangular components):
If a force is formed from two mutually perpendicular components then such components are called its perpendicular components or rectangular components.
Explanation: Consider a force F is making an angle “θ” along “x”- axis. Draw its perpendicular components represented by “OB” and “AB” drawn in two perpendicular lines x-axis and y-axis.
According to head to tail rule, OA is the resultant of vector represented by OB and BA.
Thus OA= OB + BA …..(1)
The components OB and BA are perpendicular to each other. They are called perpendicular components of OA represents force F. Hence OB represents its x-component “Fx” called horizontal component and BA represents its y-component Fy called its vertical component. Therefore, equation (1) can be expressed as.
F= Fx + Fy …..(2)
The magnitudes Fx and Fy can be found by using the trigonometric ratios. In right angled triangle OBA.
Horizontal component “Fx“
The component of force which is along x-axis is called x-component (or) horizontal component of force.
Cosθ = Base / Hypotenuse
Cosθ = OB / OA
.:. OB =Fx
.:. OA =F
Cosθ = Fx / F
Fx = F Cosθ …. (3)
Vertical component “Fy“
The component of force which is along y-axis is called y-component (or) vertical component of force.
Sinθ = Perpendicular / Hypotenuse
Sinθ = AB / OA
.:. AB = Fy
OA = F
.:. Sinθ = Fy/ F
Fy =F Sinθ …..(4)
Equations (3) and (4) give the perpendicular components (rectangular components) Fx and Fy respectively.
Q 4.6 When a body is said to be in equilibrium?
Ans. Equilibrium: “A body is said to be in equilibrium if no net force is acting on the body”. A body in equilibrium thus remains rest or moves with uniform velocity.
Q 4.7 Explain the first condition for equilibrium.
Ans. “A body is said to be in equilibrium if no net force is acting on the body”.
A body in equilibrium thus remains at rest or moves with uniform velocity. There are two conditions of equilibrium.
First Condition of Equilibrium: “A body is said to satisfy first condition of equilibrium if the resultant of all the forces acting on it is zero”.
Let n be the number of forces F1, F2, F3, …, Fn are acting on a body such that F! +F2+ F3 + …. + Fn = 0
Or ΣF= 0 ….. (1)
The symbol Σ is a Greek letter called sigma used for summation.
Explanation with x and y components of force:
The first condition of equilibrium can also be defined in terms of x and y-components of the force acting on the body.
Sum of x-components of force
F1x + F2x + F3x +…….+Fnx = 0
Sum of y-components of force
F1y + F2y + F3y +…….+Fny = 0
or ΣFx = 0
i.e sum of all the X-components of forces is equal to zero.
and ΣFy = 0
i.e sum of all the y-components of forces is equal to zero.
Examples
A book lying on a table or a picture hanging on a wall are at rest and thus satisfy first condition of equilibrium. A paratrooper coming down with terminal velocity (uniform velocity) also satisfies first condition of equilibrium.
Q 4.8 Why there is a need of second condition for equilibrium if a body a satisfies first condition for equilibrium?
Ans: Second Condition of Equilibrium
“If the sum of all the torque acting on the body is equal to zero then the body satisfies second condition of equilibrium.” Στ=0
Explanation:
Consider a body pulled by the forces F1 and F2 as shown in figure (a) both forces are equal in magnitude but opposite in direction. Hence their resultant will be zero. According to the first condition, the body will be in equilibrium.
Now shift the location of the forces as shown in figure (b) the body is not in equilibrium although the first condition of equilibrium is still satisfied. It is because the body has tendency to rotate. This situation demands another condition for equilibrium in addition to the first condition for equilibrium. That’s why we need second condition of equilibrium.
Q 4.9 What is second condition for equilibrium. Write its formula.
Ans. If the sum of all the torque acting on the body is equal to zero then the body satisfies the second condition of equilibrium.” i.e. Στ=0.
Q 4.10 Give an example of a moving body which is in equilibrium.
Ans. (i) A paratrooper coming down with terminal velocity is in equilibrium because his weight is in downward direction is equal to the force of friction of air in upward direction. Paratroopers is moving with uniform velocity, so the paratrooper is in equilibrium.
(ii) An object is moving with uniform velocity having zero acceleration is an example of equilibrium.
(iii) A car moving with uniform velocity on leveled road is the example of equilibrium.
Q 4.11 Think of a body which is at rest but not in equilibrium.
Ans. In simple pendulum when the pendulum is at extreme position it is at rest for a while but at that time gravitational force remains acting on it. So the pendulum is at rest but not in equilibrium. When a ball is thrown vertically upward it comes to rest at the top position before falling towards ground. At that position ball is at rest but not in equilibrium.
Q 4.12 Why a body cannot be in equilibrium due to single force acting on it?
Ans. When a single force acts on a body, body moves in the direction of force. This force is not balanced by any other force. Hence body is not in equilibrium when a single force acts on a body. It produces motion as well as rotation in a body.
Q 4.13 Why the height of vehicles is kept as low as possible?
Ans. We know that position of centre of mass of an object plays an important role in their stability. To get stability their centre of mass must be kept as low as possible so it is the reason that height of vehicle is kept as low as possible.
Q 4.14 Explain what is meant by stable, unstable and neutral equilibrium. Give one examples in each case.
Ans. There are three states of equilibrium
- Stable equilibrium
- Unstable equilibrium
- Neutral equilibrium
A body may be in one of these three states of equilibrium.
Stable Equilibrium
A body is said to be in stable equilibrium if after a slight tilt it returns to its previous position.”
Example:
Consider a book lying on the table. Tilt the book slightly about its one edge by lifting it from the opposite side. It returns to its previous position when sets free. Such a state of the body is called stable equilibrium.
Explanation:
When a body is in stable equilibrium, its centre of gravity is at the lowest position. When it is tilted, its centre of gravity rises. It returns to its stable state by lowering its centre of gravity. A body remains in stable equilibrium as long as the centre of gravity acts through the base of the body.
Consider a block as shown in fig (a). When the block is tilted, its centre of gravity G rises. If the vertical line through G passes through its base in the tilted position as shown in fig (b), the block returns to its initial position. If the vertical line through G gets out of its base as shown in figure (c), the block does not return to its previous position. It topples over its base and moves to new stable equilibrium position.
Unstable Equilibrium
“A body does not return to its previous position when sets free after a slightest tilt is said to be in unstable equilibrium”.
Example:
Take a pencil and try to keep it in the vertical position on its in tip as shown in figure. Whenever you leave it, the pencil topples over about its tip and falls down. This is called the unstable equilibrium. In unstable equilibrium, the centre of gravity of the body is at highest position in the state of unstable equilibrium. As the body topples over about its base (tip), its centre of gravity moves towards its lower position and does not return to its previous position.
Neutral Equilibrium:
“A body remains in its new position when disturbed from its previous position, it is said to be in the state of neutral equilibrium. In this state, centre of gravity remains at the same position.”
Explanation:
Take a ball and place it on a horizontal surface as shown in figure. Roll the ball over the surface and leave it after displacing from its initial position. It remains in its new position and does not return to its initial position. This is called neutral equilibrium.
There are various objects which have neutral equilibrium such as a ball, a sphere, a roller, a pencil lying horizontally, an egg lying horizontally on a flat surface etc.
