A geometrical and harmonic progression have the same pth, qth ,rth terms a,b,c respectively. Show that a(b-c) log a + b(c-a) log b + c(a-b) log c =0.
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Two small discs of masses m1 and m2 interconnected by a
weightless spring rest on a smooth horizontal plane. The discs are
set in motion with initial velocities v1 and v2 whose directions are
mutually perpendicular and lie in a horizontal plane. Find the total
energy of this system in the frame of the centre of inertia.
A stationary pulley carries a rope whose one end supports
a ladder with a man and the other end the counterweight of mass M.
The man of mass m climbs up a distance l' with respect to the ladder
and then stops. Neglecting the mass of the rope and the friction in
the pulley axle, find the displacement l of the centre of inertia of
The reference frame, in which the centre of inertia of a given
system of particles is at rest, translates with a velocity V relative
to an inertial reference frame K. The mass of the system of particles
equals m, and the total energy of the system in the frame of the centre
of inertia is equal to E. Find the total energy E of this system of
particles in the reference frame K.
A point A is located on the rim of a wheel of radius R
0.50 m which rolls without slipping along a horizontal surface
with velocity v = 1.00 m/s. Find:
(a) the modulus and the direction of the acceleration vector of the
(b) the total distance s traversed by the point A between the two
successive moments at which it touches the surface.