Classical Mechanics MCQs Question and Answer in Engineering Physics Page-2 section-1

11.
The moment of inertia of a uniform sphere of radius, r about an axis passing through its centre is given by $$\frac{2}{5}\left( {\frac{{4\pi }}{3}{r^5}\rho } \right).$$ A rigid sphere of uniform mass density $$\rho $$ and radius R has two smaller spheres of radii $$\frac{R}{2}$$ hollowed out of it as shown in the figure given below.

The moment of inertia of the resulting body about Y-axis is

A. $$\frac{{\pi \rho {R^5}}}{4}$$

B. $$\frac{{5\pi \rho {R^5}}}{{12}}$$

C. $$\frac{{7\pi \rho {R^5}}}{{12}}$$

D. $$\frac{{3\pi \rho {R^5}}}{4}$$

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12.
The mass m of a moving particle is $$\frac{{2{m_0}}}{{\sqrt 3 }},$$ where m₀ is rest mass. The linear momentum of the particle is

A. 2m₀c

B. $$\frac{{2{m_0}}}{{\sqrt 3 }}$$

C. m₀c

D. $$\frac{{{m_0}c}}{{\sqrt 3 }}$$

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13.
A space station moving in a circular orbit around the earth goes into a new bound orbit by fixing its engine radially outwards. This orbit is

A. larger circle

B. smaller circle

C. an ellipse

D. a parabola

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14.
A particle of mass m is attached to a thin uniform rod of length a and mass 4m. The distance of the particle from the centre of mass of the rod is $$\frac{a}{2}.$$

The moment of inertia of the combination about an axis passing through a normal to the rod is

A. $$\frac{{64}}{{48}}m{a^2}$$

B. $$\frac{{91}}{{48}}m{a^2}$$

C. $$\frac{{27}}{{48}}m{a^2}$$

D. $$\frac{{51}}{{48}}m{a^2}$$

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15.
The Poisson bracket between $$\theta $$ and $${\dot \theta }$$ is

A. $$\left\{ {\theta ,\,\dot \theta } \right\} = 1$$

B. $$\left\{ {\theta ,\,\dot \theta } \right\} = \frac{1}{{m{L^2}}}$$

C. $$\left\{ {\theta ,\,\dot \theta } \right\} = \frac{1}{m}$$

D. $$\left\{ {\theta ,\,\dot \theta } \right\} = \frac{g}{L}$$

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16.
If p and q are the position and momentum variables, which one of the following is not canonical transformation?

A. Q = αq and P = $$\frac{p}{\alpha }$$, for α ≠ 0

B. Q = αq + βp and P = βq + αp, for α, β real and α² - β² = 1

C. Q = p and P = q

D. Q = p and P = -q

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17.
A rigid body is rotating about its centre of mass; fixed at origin with an angular velocity $$\overrightarrow \omega $$ and angular acceleration $$\overrightarrow \alpha $$. If the torque acting on it is $$\overrightarrow \tau $$ and its angular momentum is $$\overrightarrow {\bf{L}} $$, then the rate of change of its kinetic energy is

A. $$\frac{1}{2}\overrightarrow \tau \cdot \overrightarrow \omega $$

B. $$\frac{1}{2}\overrightarrow {\bf{L}} \cdot \overrightarrow \omega $$

C. $$\frac{1}{2}\left( {\overrightarrow \tau \cdot \overrightarrow \omega + \overrightarrow {\bf{L}} \cdot \overrightarrow \alpha } \right)$$

D. $$\frac{1}{2}\overrightarrow {\bf{L}} \cdot \overrightarrow \alpha $$

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18.
The homogeneity of time leads to the law of conservation of (a)

A. linear momentum

B. angular momentum

C. energy

D. parity

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19.
A rigid frictionless rod rotates anticlockwise in a vertical plane with angular velocity $$\overrightarrow \omega $$. A bead of mass m moves outward along the rod with constant velocity $$\overrightarrow {{u_0}} $$ . The bead will experience a coriolis force

A. $$2{m_0}u\omega \hat \theta $$

B. $$ - 2m{u_0}\omega \hat \theta $$

C. $$4m{u_0}\omega \hat \theta $$

D. $$ - m{u_0}\omega \hat \theta $$

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20.
The Lagrangian for a three-particle system is given by $$L = \frac{1}{2}\left( {\dot n_1^2 + \dot n_2^2 + \dot n_3^2} \right) - {a^2}\left( {n_1^2 + n_2^2 + n_3^2 - {n_1}{n_3}} \right)$$
where, a is real, then one of the normal coordinates has a frequency $$\omega $$ given by

A. $${\omega ^2} = {a^2}$$

B. $${\omega ^2} = \frac{{{a^2}}}{2}$$

C. $${\omega ^2} = 2{a^2}$$

D. $${\omega ^2} = \sqrt 2 {a^2}$$

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Classical Mechanics MCQs Question and Answer in Engineering Physics

Answer & Solution

12. The mass m of a moving particle is $$\frac{{2{m_0}}}{{\sqrt 3 }},$$ where m0 is rest mass. The linear momentum of the particle is

Answer & Solution

13. A space station moving in a circular orbit around the earth goes into a new bound orbit by fixing its engine radially outwards. This orbit is

Answer & Solution

14. A particle of mass m is attached to a thin uniform rod of length a and mass 4m. The distance of the particle from the centre of mass of the rod is $$\frac{a}{2}.$$ The moment of inertia of the combination about an axis passing through a normal to the rod is

Answer & Solution

15. The Poisson bracket between $$\theta $$ and $${\dot \theta }$$ is

Answer & Solution

16. If p and q are the position and momentum variables, which one of the following is not canonical transformation?

Answer & Solution

Answer & Solution

18. The homogeneity of time leads to the law of conservation of (a)

Answer & Solution

19. A rigid frictionless rod rotates anticlockwise in a vertical plane with angular velocity $$\overrightarrow \omega $$. A bead of mass m moves outward along the rod with constant velocity $$\overrightarrow {{u_0}} $$ . The bead will experience a coriolis force

Answer & Solution

20. The Lagrangian for a three-particle system is given by $$L = \frac{1}{2}\left( {\dot n_1^2 + \dot n_2^2 + \dot n_3^2} \right) - {a^2}\left( {n_1^2 + n_2^2 + n_3^2 - {n_1}{n_3}} \right)$$ where, a is real, then one of the normal coordinates has a frequency $$\omega $$ given by

Answer & Solution

12.
The mass m of a moving particle is $$\frac{{2{m_0}}}{{\sqrt 3 }},$$ where m₀ is rest mass. The linear momentum of the particle is

13.
A space station moving in a circular orbit around the earth goes into a new bound orbit by fixing its engine radially outwards. This orbit is

14.
A particle of mass m is attached to a thin uniform rod of length a and mass 4m. The distance of the particle from the centre of mass of the rod is $$\frac{a}{2}.$$

The moment of inertia of the combination about an axis passing through a normal to the rod is

15.
The Poisson bracket between $$\theta $$ and $${\dot \theta }$$ is

16.
If p and q are the position and momentum variables, which one of the following is not canonical transformation?

18.
The homogeneity of time leads to the law of conservation of (a)

19.
A rigid frictionless rod rotates anticlockwise in a vertical plane with angular velocity $$\overrightarrow \omega $$. A bead of mass m moves outward along the rod with constant velocity $$\overrightarrow {{u_0}} $$ . The bead will experience a coriolis force

20.
The Lagrangian for a three-particle system is given by $$L = \frac{1}{2}\left( {\dot n_1^2 + \dot n_2^2 + \dot n_3^2} \right) - {a^2}\left( {n_1^2 + n_2^2 + n_3^2 - {n_1}{n_3}} \right)$$
where, a is real, then one of the normal coordinates has a frequency $$\omega $$ given by