This document contains questions related to mechanics topics including center of mass, linear momentum, torque, angular momentum, moment of inertia, and conservation of angular momentum. It begins by asking questions about defining and deriving expressions for the position vector of the center of mass for single particles, two-particle systems, and N-particle systems. It then discusses linear momentum, torque, angular momentum, moment of inertia, and the relationships between these quantities. It concludes by stating the principle of conservation of angular momentum and asking for examples.

1. For CBSE as well GSEB Board

2. 1. Define centre of mass of (i) a body (ii) two-
particle system (iii) N-particle system.
2. Derive an expression for the position vector
of the centre of mass of “TWO-particle
system
3. Derive an expression for the position vector
of the centre of mass of a system of N
particles
4. A system consists of N particles of total
mass M. Show that the centre of mass
moves like a particle of total mass M under
the influence of the net external force.

3. 1. Show that the total linear momentum of
a system of particles is equal to the
product of total mu of the system and
the velocity of centre of mass of the
system.
2. Show that if the net external force on a
system of particles is zero, the velocity
of the center mass of the system is
constant.
3. Derive an expression for the work done
by a force on a particle in a plane. How
does it lead to the definition of torque
due to a force?

4. 1. Show that torque produced by a force is
equal to the cross product of the position
force and the force.
2. Derive the relation between torque and
angular momentum of a particle about an
axis
3. Give Geometrical meaning of Angular
Momentum
4. Deduce Kepler’s Second law of planetary
Motion from angular momentum
consideration

5. 1. Define and explain moment of inertia of a
body about an axis of rotation.
2. What is radius of gyration of a body? What is
its significance?
3. State and prove theorem of parallel axes.
4. State and prove theorem of perpendicular
axes.
5. Derive an expression for the moment of
inertia of a uniform thin rod about an axis
through its centre and perpendicular to its
length.

6. 1. Derive an expression for the moment of
inertia of a uniform ring about an axis
passing through the centre of the ring and
perpendicular to the plane of the ring.
2. Derive an expression for the moment of
inertia of a uniform disc about an axis
through the centre of the disc and
perpendicular to the plane of the disc.
3. Obtain an expression for the kinetic
energy of a rotating body

7. 1. Derive the relation between angular
momentum and moment of inertia of a body
about the axis of rotation.
2. Prove the relation τ = lα where the symbols
have their usual meanings.
3. State and explain principle of conservation
of angular momentum. Give two practical
examples.