Classical Mechanics MCQs Question and Answer in Engineering Physics Page-4 section-1

31.
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

A. five

B. four

C. two

D. one

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32.
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. 6.4 × 10^-6 s

B. 0.62 × 10^-6 s

C. 2.16 × 10^-6 s

D. 0.19 × 10^-6 s

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33.
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

A. $$\frac{{2\left( {1 + \dot q} \right)}}{{{q^3}}}$$

B. $$\frac{{2\left( {1 - \dot q} \right)}}{{{q^3}}}$$

C. $$\frac{2}{{{q^3}}}$$

D. $$\frac{{\dot q}}{{{q^3}}}$$

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34.
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. 6

B. 5

C. 2

D. $$\frac{8}{3}$$

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35.
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

A. ω

B. > ω

C. < ω

D. directly proportional to acceleration

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36.
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

A. $$M\sqrt {Gmb} $$

B. $$b\sqrt {GmM} $$

C. $$G\sqrt {mMb} $$

D. $$m\sqrt {2GMb} $$

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37.
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

A. $${{\ddot x}_1} + {\omega _0}^2{x_1} = {\omega _0}^2\mu {x_1},\,{{\ddot x}_2} + {\omega _0}^2{x_2} = {\omega _0}^2\mu {x_2}$$

B. $${{\ddot x}_1} + {\omega _0}^2{x_1} = {\omega _0}^2\mu {x_2},\,{{\ddot x}_2} + {\omega _0}^2{x_2} = {\omega _0}^2\mu {x_1}$$

C. $${{\ddot x}_1} + {\omega _0}^2{x_1} = {\omega _0}^2\mu {x_1},\,{{\ddot x}_2} + {\omega _0}^2{x_2} = - {\omega _0}^2\mu {x_2}$$

D. $${{\ddot x}_1} + {\omega _0}^2{x_1} = {\omega _0}^2\mu {x_1},\,{{\ddot x}_2} + {\omega _0}^2{x_2} = {\omega _0}^2\mu {x_1}$$

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38.
Which one of the following is true for the above system?

A. The acceleration of the comet is maximum when it is closest to the sun

B. The linear momentum of the comet is constant

C. The comet will return to the solar system after a special period

D. The kinetic energy of the comet is a constant

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39.
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

A. ω, $$\sqrt 3 $$ ω and $$\sqrt 3 $$ ω

B. $$\sqrt 2 $$ ω, $$\sqrt 3 $$ ω and $$\sqrt 3 $$ ω

C. $$\sqrt 2 $$ ω, $$\sqrt 2 $$ ω and 2ω

D. $$\sqrt 2 $$ ω, 2ω and 2ω

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40.
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

A. central and conservative

B. non-central and conservative

C. central and non-conservative

D. non-central and non-conservative

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Classical Mechanics MCQs Question and Answer in Engineering Physics

Answer & Solution

32. 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

Answer & Solution

33. 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

Answer & Solution

34. 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

Answer & Solution

35. 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

Answer & Solution

36. 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

Answer & Solution

37. 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

Answer & Solution

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

Answer & Solution

39. 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

Answer & Solution

Answer & Solution

32.
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

33.
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

34.
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

35.
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

36.
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

37.
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

38.
Which one of the following is true for the above system?

39.
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