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182 PHYSICS

velocities taken relative to the centre of mass. Remember ′ =r r – R ; rest of the
i i
notation is the standard notation used in the chapter. Note ′ L and M ×R V can
be said to be angular momenta, respectively, about and of the centre of mass of
the system of particles.
d ′ d ′
p
L
(d) Show = ∑ r i ′ ×
dt dt
Further, show that
d ′
L
= ′ ττ
dt ext
where ′ τ ττ τ ext is the sum of all external torques acting on the system about the
centre of mass.
(Hint : Use the definition of centre of mass and third law of motion. Assume the
internal forces between any two particles act along the line joining the particles.)

Pluto - A Dwarf Planet

The International Astronomical Union (IAU) at the IAU 2006 General Assembly
held on August 24, 2006, in Prague in Czech Republic, adopted a new
definition of planets in our Solar System. According to the new definition,
Pluto is no longer a planet. This means that the Solar System consists of
eight planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and
Neptune. According to the IAU usage, the ‘planet’ and ‘other bodies’ in our
Solar System, except satellites, are to be defined into three distinct categories
of celestial objects in the following way:
1. A ‘planet’ is a celestial body that (a) is in orbit around the Sun, (b) has
sufficient mass for its self-gravity to overcome rigid body forces so that it
assumes a hydrostatic equilibrium (nearly round) shape, and (c) has
cleared the neighbourhood around its orbit.
2. A ‘dwarf planet’ is a celestial body that (a) is in orbit around the Sun,
(b) has sufficient mass for its self-gravity to overcome rigid body forces so
that it assumes a hydrostatic equilibrium (nearly round) shape, (c) has
not cleared the neighbourhood around its orbit, and (d) is not a satellite.

3. All ‘other objects’, except satellites, orbiting the Sun, shall be referred to
collectively as ‘Small Solar-System Bodies’.

Unlike other eight planets in the Solar System, Pluto’s orbital path overlaps
with ‘other objects’ and the planet Neptune. The ‘other objects’ currently
include most of the Solar System asteroids, most of the Trans-Neptunian
Objects (TNOs), comets, and other small bodies.
Pluto is a ‘dwarf planet’ by the above definition and is recognised as the
prototype of a new category of Trans-Neptunian Objects.

2018-19