Case Study Questions Class 11 Physics Chapter 7 Systems of particles and rotational motion
CBSE Class 11 Case Study Questions Physics Systems of particles and rotational motion. Important Case Study Questions for Class 11 Board Exam Students. Here we have arranged some Important Case Base Questions for students who are searching for Paragraph Based Questions Systems of particles and rotational motion.
At Case Study Questions there will given a Paragraph. In where some Important Questions will made on that respective Case Based Study. There will various types of marks will given 1 marks, 2 marks, 3 marks, 4 marks.
CBSE Case Study Questions Class 11 Physics Systems of particles and rotational motion
Case Study – 1
The cross product of two vectors is given by Vector C = A × B. The magnitude of the vector defined from cross product of two vectors is equal to product of magnitudes of the vectors and sine of angle between the vectors. Direction of the vectors is given by right hand corkscrew rule and is perpendicular to the plane containing the vectors.
∴ |vector C| = ABsinθ and Vector C = ABsinθ n
Where, cap n is the unit vector perpendicular to the plane containing the vectors A and B. Following are properties of vector product
a) Cross product does not obey commutative law. But its magnitude obeys commutative low.
c) It obeys distributive law
d) The magnitude cross product of two vectors which are parallel is zero. Since θ = 0;
vector |A x B| = AB sin 0° = 0
e) For perpendicular vectors, θ = 90°, vector |A x B| = AB sin 90° |cap n| = AB
î x î = ĵ x ĵ = ƙ x ƙ = 0
î x ĵ = ƙ; ĵ x ƙ = î; ƙ x î = ĵ
ĵ x î = – (î x ĵ) = – ƙ ; ƙ x ĵ = – (ĵ x ƙ) = – î ; î x ƙ = – (ƙ x î) = – ĵ
f) The expression for a × b can be put in a determinant form which is easy to remember
Answer the following questions from above case study.
1) If θ is angle between two vectors then resultant vector is maximum when θ is
a) 0
b) 90
c) 180
d) None of these
2) Cross product is operation performed between
a) Two scalar numbers
b) One scalar other vector
c) 2 vectors
d) None of these
3) Define cross product of two vectors
4) State right hand screw rule for finding out direction of resultant after cross product of two vectors.
5) Give properties of cross product of parallel vector.
Answer key-1
1) a
2) c
3) The cross product of two vectors is given by Vector C = A × B. The magnitude of the vector defined from cross product of two vectors is equal to product of magnitudes of the vectors and sine of angle between the vectors.
∴ |vector C| = ABsinθ and Vector C = ABsinθ n. Where, cap n is the unit vector perpendicular to the plane containing the vectors A and B.
4) We can find the direction of the unit vector with the help of the right-hand rule. In this rule, we can stretch our right hand so that the index finger of the right hand in the direction of the first vector and the middle finger is in the direction of the second vector. Then, the thumb of the right hand indicates the direction or unit vector n.
5) The cross product of two vectors is zero vectors if both the vectors are parallel or opposite to each other. Conversely, if two vectors are parallel or opposite to each other, then their product is a zero vector. Two vectors have the same sense of direction. θ = 900 As we know, sin 0° = 0 and sin 90° = 1
Case Study – 2
Radius of gyration: The radius of gyration of a body about an axis may be defined as the distance from the axis of a mass point whose mass is equal to the mass of the whole body and whose moment of inertia is equal to the moment of inertia of the body about the axis.
the moment of inertia of a rigid body analogous to mass in linear motion and depends on the mass of the body, its shape and size; distribution of mass about the axis of rotation, and the position and orientation of the axis of rotation.
Theorem of perpendicular axes
It states that the moment of inertia of a planar body (lamina) about an axis perpendicular to its plane is equal to the sum of its moments of inertia about two perpendicular axes concurrent with perpendicular axis and lying in the plane of the body. If we consider a planar body, An axis perpendicular to the body through a point O is taken as the z-axis. Two mutually perpendicular axes lying in the plane of the body and concurrent with z-axis, i.e., passing through O, are taken as the x and y-axes. The theorem states that
I z = I x + I y.
Theorem of parallel axes
The moment of inertia of a body about any axis is equal to the sum of the moment of inertia of the body about a parallel axis passing through its centre of mass and the product of its mass and the square of the distance between the two parallel axes.
z and z’ are two parallel axes, separated by a distance a. The z-axis passes through the centre of mass O of the rigid body. Then according to the theorem of parallel axes
Iz’= Iz + Ma2
Where Iz and Iz’ are the moments of inertia of the body about the z and z¢ axes respectively, M is the total mass of the body and a is the perpendicular distance between the two parallel axes.
1) SI unit of radius of gyration
a) Metre (m)
b) M2
c) M3
d) None of these
2) Moment of inertia is analogous to
a) Mass
b) Area
c) Force
d) None of these
3) Define radius of gyration
4) State Theorem of perpendicular axes
5) State Theorem of parallel axes
Answer key – 2
1) a
2) a
3) Radius of gyration: The radius of gyration of a body about an axis may be defined as the distance from the axis of a mass point whose mass is equal to the mass of the whole body and whose moment of inertia is equal to the moment of inertia of the body about the axis.
4) Theorem of perpendicular axes
It states that the moment of inertia of a planar body (lamina) about an axis perpendicular to its plane is equal to the sum of its moments of inertia about two perpendicular axes concurrent with perpendicular axis and lying in the plane of the body. If we consider a planar body, an axis perpendicular to the body through a point O is taken as the z-axis. Two mutually perpendicular axes lying in the plane of the body and concurrent with z-axis, i.e., passing through O, are taken as the x and y-axes. The theorem states that
I z = I x + I y
5) The moment of inertia of a body about any axis is equal to the sum of the moment of inertia of the body about a parallel axis passing through its centre of mass and the product of its mass and the square of the distance between the two parallel axes. z and z’ are two parallel axes, separated by a distance a. The z-axis passes through the centre of mass O of the rigid body. Then according to the theorem of parallel axes
Iz’= Iz + Ma2
Where Iz and Iz’ are the moments of inertia of the body about the z and z¢ axes respectively, M is the total mass of the body and a is the perpendicular distance between the two parallel axes.
Class 11 Physics Systems of Particles and Rotational Motion