If the roots of 10x^3cx^254x27 0 are in harmonic progression, then find c and all the roots.
Rushabh Jain
@Rushabh Jain
Best posts made by Rushabh Jain

Sequence and series

Sequence and series
If a,b,c be in geometric progression and log a, log b, log c be in arithmetic progression, then show that the common difference of the arithmetic progression must be 3/2.

kinematics
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
point A;
(b) the total distance s traversed by the point A between the two
successive moments at which it touches the surface. 
Sequence and series
A geometrical and harmonic progression have the same pth, qth ,rth terms a,b,c respectively. Show that a(bc) log a + b(ca) log b + c(ab) log c =0.

Rotational motion
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. 
Sequence and series
Find the condition that the roots iof the equation x^3px^2+qxr=0 may be in arithmetic progression and hence solve the equation x^312x^2+ 39x28=0.

Rotational motion
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
this system. 
Sequence and series
Prove that if a,b,c are in geometric progression then log a, log b , log c are in arithmetic progression and ots converse is also true.

Rotational motion
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.
Latest posts made by Rushabh Jain

Gravitation
Derive the relationship between gravitational force to planets inertial force?

Gravitation
Derive the relationship between gravitational force to planets inertial force? Explain newton inertial force law with examples.

Gravitation
uresh was struggling to understand Kepler's second law of planetary motion. Then his
friend Ravi explained to him how the planets move around Sun obeying Kepler's laws of
planetary motion.
(a) Comment upon the values of Ravi. 
Gravitation
If the earth suddenly stopped in its orbit assumed to be circular, find the time
that would elapse before it falls into the sun. 
Kinematics
Q. Consider the “pedagogical machine” of the previous problem in
the case where F is zero. Find the acceleration of M1. 
Kinematics
A disk rotates with constant angular velocity ω, as shown. Two
masses, mA and mB, slide without friction in a groove passing
through the center of the disk. They are connected by a light string
of length l, and are initially held in position by a catch, with mass
mA at distance rA from the center. Neglect gravity. At t = 0 the
catch is removed and the masses are free to slide.
Find ¨ra immediately after the catch is removed, in terms of mA,
mB, l, rA, and ω.