A mass m is constrained to move on a horizontal frictionless surface. It is set in circular motion with radius r0 and angular speed ω0 by an applied force $$\overrightarrow {\bf{F}} $$ communicated through an inextensible thread that passesthrough a hole on the surface as shown in figure given below. Then, this force is suddenly doubled.
Classical Mechanics mcq question image
The magnitude of the radial velocity of the mass

The speed of a particle whose kinetic energy is equal to its rest mass energy, is given by (c is the speed of light in vacuum)

The Hamiltonian corresponding to the Lagrangian $$L = a{{\dot x}^2} + b{{\dot y}^2} - kxy$$     is

An object of mass m rests on a surface with coefficient of static friction μ. Which of the following is not correct?

Two solid spheres of radius R and mass M each are connected by a thin rigid rod of negligible mass. The distance between the centre is 4R. The moment of inertia about an axis passing through the centre of symmetry and perpendicular to the line joining the sphere is

A circular hoop of mass M and radius a rolls without slipping with constant angular speed ω along the horizontal X-axis in the X-Y plane. When the hoop is at a distance d = $$\sqrt 2 $$ a from the origin, the magnitude of the total angular momentum of the hoop about the origin is

Hamiltonian canonical equations of motion for a conservation system are

A cylinder of mass M and radius R is rolling down without slipping on an inclined plane of angle of inclination θ. The number of generalised coordinate required to describe the motion of the system is

A particle moves in a central force field $$\overrightarrow {\bf{F}} = k{r^n}{\bf{\hat r}},$$   where k is constant, r is distance of the particle from the origin and $${{\bf{\hat r}}}$$ is the unit vector in the direction of $$\overrightarrow {\bf{r}} $$. Closed stable orbits are possible for