Classical Mechanics MCQs Question and Answer in Engineering Physics

Two particles of equal masses are connected by an inextensible string of length L. One of the masses is constrained to moves on the surface of a horizontal table. The string passes through a small hole in the table and the other mass is hanging below the table. The only constraint is that the first mass moves on the surface of the table. The number of degree of freedom of the masses string system is

Assuming the mean life, of a muon (in its rest frame) to be 2 × 10^-6 s, its life time in the laboratory frame, when it is moving with a velocity 0.95 c is

A particle is moving under the action of a generalised potential $$V\left( {q,\,\dot q} \right) = \frac{{\left( {1 + \dot q} \right)}}{{{q^2}}}$$
The magnitude of generalised force is

The moment of inertia tensor of a rigid body is given by \[I = \left[ {\begin{array}{*{20}{c}} 8&0&{ - 4} \\ 0&4&0 \\ { - 4}&0&8 \end{array}} \right]\]
Moment of inertia a out an axis $${\bf{\hat n}} = \left( {\frac{1}{2},\,\frac{{\sqrt 3 }}{2},\,0} \right)$$   is

A closed tall jar containing air and a fly placed on a sensitive weighing machine when the fly is stationary, the reading of the weighing machine is ω. If the fly starts with some upward acceleration, the reading of the machine will be

Consider a comet of mass m moving in a parabolic orbit around the sun. The closets distance between the comet and the sun is b, the mass of the sun is M and universal gravitation constant is G. The angular momentum of the comet is

The Lagrangian of two coupled oscillators of mass m each is $$L = \frac{1}{2}\left( {{{\dot x}_1}^2 + {{\dot x}_2}^2} \right) - \frac{1}{2}m{\omega _0}^2\left( {{x_1}^2 + {x_2}^2} \right) + m{\omega _0}^2\mu {x_1}{x_2}$$
The equations of motion are

Which one of the following is true for the above system?

A particle of mass m is moving in a potential of the form V(x, y, z) = $$\frac{1}{2}$$ mω² (3x² + 3y² + 2z² + 2xy). The oscillation frequencies of the three normal modes of the particle are given by

Consider two particles with position vectors $$\overrightarrow {{{\bf{r}}_1}} $$ and $$\overrightarrow {{{\bf{r}}_2}} $$ . The force exerted by particle 2 on particle 1 is $$\overrightarrow {\bf{F}} \left( {\overrightarrow {{{\bf{r}}_1}} ,\,\overrightarrow {{{\bf{r}}_2}} } \right) = \left( {{{{\bf{\dot r}}}_2} - {{{\bf{\dot r}}}_1}} \right)\left( {{r_2} - {r_1}} \right).$$       The force is