Classical Mechanics 1

A particle is constrained to move along the inner surface of a fixed hemispherical bowl. The number of degrees of freedom of the particle is

• one

• two

• three

• four

A particle moving in parabolic path the number of degree of freedom is

• one

• two

• three

• four

The homogeneity of time leads to the law of conservation of

• linear momentum

• Angular momentum

• energy

• parity

The isotropy of space leads to the law of conservation of

• linear momentum

• angular momentum

• energy

• parity

If the generalized coordinate is angle then the generalized force has the dimensions of

• force

• momentum

• torque

• energy

The constraints on a bead on a uniformly rotating wire in a force-free space are

• Rheonomous

• Scleronomous

• both

• none

The dimensions of generalized momentum are

• those of linear momentum

• those of angular momentum

• may be both

• none

If Lagrangian does not depend upon the time explicitly then

• Hamiltonian is constant

• hamiltonian is not constant

• kinetic energy is constant

• potential energy is constant

The product of generalized coordinate and its conjugate momentum has the dimensions of

• force

• energy

• angular momentum

• linear momentum

If a coordinate corresponds to a rotation is cyclic, rotation about the given axis is invariant, then following quantity is conserved

• Linear Momentum

• Angular Momentum

• kinetic energy

• Potential energy