# 11th Class Physics Chapter 2 Vectors And Equilibrium Short Question Answers

## 11th Class Physics Chapter 2 Vectors And Equilibrium Short Question Answers Below

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1.Define the Terms: (i)Unit vector (ii) Position vector (iii)Compontents of a vactor?
2.The vector sum of three vectors gives a zero resultant. What can be the orientation of the vectors?
If three vectors are such that they can be represented by the three sides of a triangle taken in cyclic order then the vector sum of the three vectors will be zero.i.e.
3.If one of the components of a vector is not zero can its magnitude be zero?
4. can a vector have a component greater than the vector’s magnitude?
No,component of a vector cannot have magnitude greater than the magnitude of the vectors itself because  component is always a part of the resultant vector so the magnitude if the component will be less than that of resultant vector.Of course if the two vectors of the same magnitude act at an angle of 120 with each other then
C=A+B
[ C]=[ A]=[ B]
where modulus [ C],[ A],[ B] indicate the magnitudes of vector   C,A,Brespectively.
Hence the maximum value of magnitude of component can be equal to the magnitude of the resultant vector.
5.Can the magnitude of a vector have a negative value?
6.Under what circumstances would a vector have components that are equal in magnitude?
If a certain vector A makes an angle of 45ᵒ with horizontal axis (x-axis) the magnitude of the rectangular components will be
Ax=A cos0=Acos45ᵒ
= A×0.707
or Ax=0.707 A…………..(i)
and
Ay=Asin45ᵒ  = A×0.707
or Ay=0.707 A…………… (ii)
Equations (i) and (ii) show that a vector will have components of equal magnitude if it makes an angle of 45ᵒ with x-axis
7.Is it possible to add a vector quantity to a scalar quantity?
No, it is not possible to add a vector quantity to a scalar quantity because these are two different physical quantities.Physical quantities of the same nature can be added for example vectors of same nature can be added geocentrically to give a resultant vectors but scalar quantities of the same nature can be added algebraically and arithmetically for their resultant. Hence two different physical quantities cannot be added.
8.Can you add zero to a null vector?
No,zero cannot be added to a null vector because zero is scalar and scalars cannot be added to the vectors.
9.Two vectors have unequal magnitudes.Can their sum be zero?
No their sum cannot be zero.Two vectors of unequal magnitudes can never be combined to give zero resultant whatever their orientation may be.Of course the sum of two vectors can be zero if both of them are equal and in opposite direction.Thus different directions cannot give zero result.
10.How would the two vectors of the same magnitude have to be oriented if they were to be combined to given a resultant equal to a vector of the same magnitudes?
When the angle between two vectors of same magnitude is 120ᵒ the magnitude of the resultant is also the same.
11.Suppose the sides of a closed polygon represent vector arranged head to tail.What is the sum of these vectors?
As we know that the resultant of a number of vetoes which make a closed path is equal to zero.
If the vectors AB,C,D,and E are represented by the sides of a closed polygon   then they are added by using head to tail rule.Thus the sun will be zero because the tail of the first vector coincides with the head of last vector
Hence,
A+ B+C+D+ En =0
Hence the sum of vectors of closed polygon becomes zero because their resultant is represented in magnitude and direction by the closing side of the  polygon taken in opposite order.
12.If all the components of the vector A1 and A2 were reversed how would this alter A1 A ?
If all components of the vectors A1   and – A are reversed then both these vectors will be written as – A1  and A2  . Therefore,
Their cross product= – A1  A = A1  A
Hence the vector product of two vectors will remain unchanged even by reversing all the components of vectors.
13.Can a body rotate about its center of gravity under the action of its weight?
No a body cannot rotate about the center of gravity under the action of its weight.As we know that the center of gravity is that point where the whole weight of the body acts.It means that the weight passes through the axis of rotation.We have read that if a force pass through the axis of rotation,its torque due to weight will be zero because in this case the value of moment arm is zero.Hence a body cannot rotate about its center of gravity under the action of weight.
14.By how many manners the two vectors are multiplied?
There are two types of multiplication of vectors. (i) Scalar product (ii) Vector product Scalar product: When the product of two vectors results into a scalar quantity,the product is called scalar product. Vector product: When the product of two vectors results into a vector quantity the product is called vector product.
15.Define vector product?
If the product of two vectors results into a vector quantity the product is called vector product. The vector product of two vectors A→and B→ is written as A→× B→,we read it as.Hence the vector product is also called cross product.
16.Write two characteristics of scalar product?
Scalar product of two perpendicular vectors is zero.
17.Define resultant vector?
The resultant of a number of similar vectors is that single vector which would have the same effect as the combined effect of all the original vectors taken together.
18.State right hand rule to find the direction of resultant of vector product?
The right hand rule is stated as’’ The tails of the two vectors A→and B→, are placed together at some point making an angle ‘0’ .This forms a plane.The direction of the product vector( A→× B→,) is perpendicular to the plane.Now rotate the first vector A→ towards the second vector B→ through the small angle.Curl the fingers of the right hand along the direction of rotation A→ keeping the thump erect.The direction of the product vector ( A→× B→,) or n will be along the erect thumb shown in the fig.
19.What is resolution of vectors?
The process of splitting up of a single vector into two or more vectors is called resolution of vector.The vector so obtained are called the components of the original vectors and the original vector is called the resultant of the components.
The process of splitting up of a single vector into two or more vectors is called resolution of vector.The vector so obtained are called the components of the original vectors and the original vector is called the resultant of the components?
Two components of a vector which are at right angles to each other such components are called rectangular components.One of the components is along horizontal axis which is called the x-component while the other is along the vertical axis known as Y-component.
21.Show that the scalar product of two vectors is commutative?
Since, A→. B→ Abcos0…………….. (1) and B→ . A→. Bacose Or B→ . A→.= A.B cos0……………(2) Because product is scalar so we conclude from equation(1) and (2) that A→. B→= B→ . A→. It means that in scalar product the order of multiplication is meaningless.Hence scalar product is commutative.
22.Give two example of vector product?
Torque: If a force F→ is applied on a rigid body at a point whose position vector is r→ from any point of the axis about which the body rotates then the torque is given by the vector product of r→ and F→ .That is π→= r→ × F→ Angular Momentum:Angular momentum L→ is the cross product of position vector r→ and linear momentum P→.It is expressed as. L→= r→× P→.
In order to add two or more vectors by this method,the representative lines of the given vectors are drawn in sch a way that the arrow head of the first vector joins with the tail of the second vector the arrow head of the second vector joins with the tail of the third vector and so on.The vector sum is obtained by joining the line of first vector with the arrow-head of the last vector. This is known as head to tail rule method.
24.What is the physical significance of cross product A→× B→,?
The magnitude of the cross product A→× B→,represents of a parallelogram with A→ and B→,as its adjacent sides.Hence, A→× B→ represents the vector area of the parallelogram with its direction (n) along the outward normal to the plane containing the vectors A→and B→, Area of parallelogram= A→× B→, AB sin0n.
25.What is equilibrium?
If a body under the action of a number of forces is at rest or moving with uniform velocity it is said to be in equilibrium.There are two types of equilibrium. (i)Static equilibrium (ii)Dynamic equilibrium.
26.Describe two conditions of equilibrium?
:(i)First condition of Equilibrium:It is stated as:A body will be in transnational equilibrium only if the vector sum of all the forces acting on it is zero.Mathematically it can be written as: ∑ F→=0 (ii) Second condition of Equilibrium: A body will be in rotational equilibrium only if the sum of all the torques acting on the body any arbitrary axis is zero.It can be written in mathematical form as ∑ʎ=0
27.Differentiate between Transnational and rotational equilibrium?
Transnational Equilibrium:When first condition of equilibrium is satisfied.There is no linear acceleration and the body will be said in translatioonal equilibrium. Rotational Equilibrium: When second condition of equilibrium is satisfied there is no angular acceleration then the body will be said in rotational equilibrium.
28.Under what condition the body will be in complete equilibrium?
For body to be in complete equilibrium.Both the linear acceleration and angular acceleration must be zero.It means that ∑F=0 and ∑ ʎ=0
29.What do you understand by positive and negative torques?
The torque which tries to rotate the body in the anti-clockwise direction is taken as positive.The torque which tends to rotate the body in the clockwise direction is taken as negative.
30.Can a body be in equilibrium under the action of a single force?
Yes a body can be in equilibrium under the action of a single force, if the force is applied at the center of the body.
31.If the body is rotating with uniform or constant velocity,What will be the angular velocity and torque acting on the body?
Since the body is rotating with uniform angular velocity therefore the angular acceleration will be zero.Thus the torque acting on the body will also be zero.
32.How can we find the values of the rectangular components of a vector?
Let vector A→ be repented by line OP making an angle 0 with x-axis as shown in fig Axi and Ayi are Two rectangular components of vector A→. The x-component of A→ is Axi and its y-component Ayj. The magnitude of x-component of A→ is given by Ax=Acos0………………. (1) and magnitude of y-component is Ay= A sin0………………..(2) 33.What do you conclude when A→× B→, =0 Ans:As we know their A→× B→= Absin0n when 0=0ᵒ A→× B→= Ab

sin(o)n Thus A→× B→ = 0……… (1) And A→× B→= Absin180ᵒ n A→× B→ = Absin (0)n or A→× B→ = 0…………….(2) From equation (1) and (2) it is concluded that two vectors A→and B→, are parallel or anti-parallel to each other.

34.A body of mass ‘’m’’ is moving in the downward direction to an inclined plane making an angle 0 to the horizontal.Find the magnitude of the resultant force?
Ans: When the mass m is moving sown ward let F be the force of friction.Thus downward force is equal to mgsin0 as shown in fig.and F is the force in the upward direction.So resultant force=mg sin0-F .
35.With the help of diagram show that A→× B→ = - B→ A→?
As we know A→× B→= -C→ …………… (1) In the fig (a) by the application of right hand rule the direction of C→ is upward.By applying the same rule the direction of the vector product B→× A→ is.Downward as in fig (b)while the magnitude of cross product has the same value. B→ × A→= C→ – B→ × A→= C→…………. (2) Comparing equation (1) and (2) we have A→× B→= – B→ × A→ Hence it the order of the vectors in the vector product is reversed the sign of the vector product is also reversed.
36.Write down the names of two examples of scalar product?
:(1) Work: Work is defined as the scalar product of force and displacement.Since force F→and displacement d→ are two vectors but work is a scalar quantity.That is ; Work = F→. d→=Fd sos0 where 0 is the angle between the directions of F→and d→ (2) Power : Another example of scalar product is power which is define as the scalar product of forces F→ and velocity V→ That is Power: F→ V→ = FV sos0 Where ‘0’ is the angle between F→ and V→
37.Define static and dynamic equilibrium.
(i) Static equilibrium:When an object does not change its position with respect to its surroundings then it is said to be at rest or in a state of static equilibrium. (ii) Dynamic equilibrium:When body is moving with uniform velocity,it is said to be in dynamic equilibrium.
38.What is the torque of force?
Torque: It is defined as a physical quantity which produces an angular acceleration in a body about its axis of rotation.Torque is denoted by Second definition:Torque is also defined as the cross product of the force and the position vector. Let F→ be the force and r→ be the position vector.Mathematically the torque is written as ʎ→=ʎ→×F→
39.What is the torque of a force about the point lying on the axis of rotation?
The torque of a force about the point lying on the axis of rotation is zero.
40.Can the magnitude of the resultant of two vectors be greater than the sum of magnitude of individual vector?
No,the magnitude of the resultant of two vectors cannot be greater than the sum of individual vectors.The resultant of two vectors has maximum value when the two vectors are along the same line and direction.In this case the magnitude of resultant will be equal to the sum of magnitudes of the magnitude of the resultant vector will always be smaller.
41.Can we talk of a vector of zero magnitude?
Commonly we do not talk of vector of zero magnitude because we cannot decide its direction.But in vector algebra we take a vector of zero magnitude as the resultant of two equal and opposite vector of acting at one point.Such a vector is called as null vector.
42.Will the value of vector of zero magnitude?
The value of vector quantity does not change with the change of reference axes.The direction of a vector quantity is specified by the angle which it makes with any of the reference axes.The reference axes may be changed but the angle which the quantity makes with any of the axes will remain the same therefore the value of the vector quantity will be unaffected.
43.Can a force directed north balance a force directed east?
They cannot balance each other because one force is acting along x-axis i,e,directed east and the other along y-axis i.e, directed north let one force F1 and other F2 .
44.Give an example of a body which is in motion yet is in equilibrium?
Consider a paratrooper jumping from an aeroplane.After the parachute opens and falls a certain distance it moves downward thereafter with uniform velocity.At this stage the weight of the paratrooper acts downward and it is balanced by the upward reaction of air on the parachute.Thus the parachute falls with nearly uniform velocity under equilibrium.

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1. Maha says:

Is it possible to add 5 in 2?explain?

2. Ch Haris Jutt says: