1. A particle is constrained to move on the circumference of a circle. The number of degrees of freedom of the particle isonetwothreefour 2. The number of degrees of freedom of the bob of a conical pendulum isonetwothreefour 3. The number of degrees of freedom of a rigid body moving freely in three dimensional space istwothreefoursix 4. Which of the following constraint is non-holonomic?motion of a body on an inclined planerigid bodysimple pendulum with rigid supportrolling disc 5. The Constraint in a rigid body isholonomic and rheonomicnonholonomic and rheonomicholonomic and scleronomicnonholonomic and scleronomic 6. The Constraint in a simple pendulum with rigid support isholonomic and scleronomicnonholonomic and scleronomicholonomic and rheonomicnonholonomic and rheonomic 7. Generalized coordinatesdepend on each otherare independent of each otherare necessarily cartesian coordinatesare necessarily spherical coordinates 8. If a generalized coordinate has the dimension of velocity, generalized velocity has the dimension ofdisplacementvelocityaccelerationforce 9. The homogeneity of space leads to the law of conservation oflinear momentumangular momentumenergyparity 10. The isotropy of space leads to the law of conservation oflinear momentumangular momentumenergyparity 11. The homogeneity of time leads to the law of conservation oflinear momentumangular momentumenergyparity 12. The Lagrangian of a simple pendulum consisting of a bob of mass $m$ suspended by a string of length $l$ is$\frac{1}{2}ml^2\dot{\theta}^2+mgl(1-\cos\theta)$$\frac{1}{2}ml^2\dot{\theta}^2-mgl(1-\cos\theta)$$\frac{1}{2}ml^2\dot{\theta}-mgl(1-\cos\theta)$$\frac{1}{2}ml^2\dot{\theta}+mgl(1-\cos\theta)$ 13. The Lagrangian of a particle of mass $m$ moving in a plane under the influence of a central potential $V(r)$ is$\frac{1}{2}m(\dot{r}^2+r^2\dot{\theta}^2)-V(r)$$\frac{1}{2}m(\dot{r}^2+\dot{\theta}^2)-V(r)$$\frac{1}{2}m(\dot{r}^2+\dot{\theta}^2)+V(r)$$\frac{1}{2}m(\dot{r}^2+r^2\dot{\theta}^2)+V(r)$ 14. The Lagrangian for a simple harmonic oscillator with frequency $\omega$ and mass $m$ in one dimension is given by$\frac{1}{2}m(\dot{x}^2+\omega x^2)$$\frac{1}{2}m(\dot{x}^2+\omega^2x)$$\frac{1}{2}m(\dot{x}^2-\omega x^2)$$\frac{1}{2}m(\dot{x}^2-\omega^2x^2)$ 15. The Lagrangian for a charged particle moving in an electromagnetic field is$L=T+q\phi+q(\vec{v}\cdot\vec{A})$$L=T-q\phi-q(\vec{v}\cdot\vec{A})$$L=T-q\phi+q(\vec{v}\cdot\vec{A})$$L=T+q\phi-q(\vec{v}\cdot\vec{A})$ 16. The equation of motion for a simple pendulum consisting of a bob of mass $m$ suspended by a string of length $l$ is$\ddot{\theta}+\frac{g}{l}\sin\theta=0$$\dot{\theta}+\frac{g}{l}\cos\theta=0$$\ddot{\theta}-\frac{g}{l}\sin\theta=0$$\dot{\theta}-\frac{g}{l}\cos\theta=0$ 17. A bead slides on a smooth rod which is rotating about one end in a vertical plane (x-y plane) with uniform angular velocity $\omega$. The Lagrange's equation is$m\ddot{r}-mr\omega^2+mg\sin\omega t=0$$m\dot{r}+mr\omega^2+mg\sin\omega t=0$$m\dot{r}-mr\omega^2-mg\sin\omega t=0$$m\ddot{r}+mr\omega^2+mg\sin\omega t=0$ 18. The equation of motion for a mass $m$ suspended by a spring of force constant $k$ and allowed to swing vertically is$m\dot{x}+kx=0$$m\dot{x}-kx=0$$m\ddot{x}-kx=0$$m\ddot{x}+kx=0$ 19. The generalized momentum corresponding to a generalized coordinate for Lagrangial $L$ is$p_k=\frac{\partial L}{\partial {q_k}}$$p_k=\frac{\partial L}{\partial \dot{q_k}}$$p_k=-\frac{\partial L}{\partial {q_k}}$$p_k=-\frac{\partial L}{\partial \dot{q_k}}$ 20. The dimensions of generalized momentumare always those of linear momentumare always those of angular momentummay be those of linear momentum or angular momentumnone of the above 21. Whenever the Lagrangian of a system does not contain a coordinate $q_k$ explicitly and $p_k$ is the generalized momentum,$q_k$ is cyclic coordinate and $p_k$ is cyclic coordinate$q_k$ is always zero$q_k$ is cyclic coordinate and $p_k$ is constant of motion$q_k$ is cyclic coordinate and $p_k$ is not constant of motion 22. If the Lagrangian does not depend on time explicitly,the Hamiltonian is constantthe Hamiltonian can not be constantthe kinetic energy is constantthe potential energy is constant 23. If the Lagrangian of a particle moving in a plane under the influence of a central potential is $L=\frac{1}{2}m(\dot{r}^+r^2\dot{\theta}^2)$. The generalized momenta corresponding to $r$ and $\theta$ are given by$m\dot{r}$ and $mr^2\dot{\theta}$$m\dot{r}$ and $mr\dot{\theta}$$m\dot{r}^2$ and $mr^2\dot{\theta}$$m\dot{r}^2$ and $mr^2\dot{\theta}^2$ 24. If the Lagrangian of a particle of mass $m$ moving in a plane is $L=\frac{1}{2}m(v_x^2+v_y^2)+a(xv_y-yv_x)$, the canonical momenta are given by$p_x=mv_x$ and $p_y=mv_y$$p_x=mv_x+ay$ and $p_y=mv_y+ax$$p_x=mv_x-ay$ and $p_y=mv_y+ax$$p_x=mv_x-ay$ and $p_y=mv_y-ax$ 25. The Hamiltonian corresponding to the Lagrangian $L=ax^2+by^2-kxy$ is$\frac{p_x^2}{2a}+\frac{p_y^2}{2b}+kxy$$\frac{p_x^2}{4a}+\frac{p_y^2}{4b}-kxy$$\frac{p_x^2}{4a}+\frac{p_y^2}{4b}+kxy$$\frac{p_x^2}{2a}+\frac{p_y^2}{2b}-kxy$ 26. The Hamiltonian of a particle of mass $m$ moving in a plane under the influence of a central potential $V(r)$ is$\frac{1}{2m}(p_r^2+\frac{p_{\theta}^2}{r^2})+V(r)$$\frac{1}{2m}(p_r^2+\frac{p_{\theta}^2}{r^2})-V(r)$$\frac{1}{2m}(\frac{p_r^2+ p_{\theta}^2}{r^2})+V(r)$$\frac{1}{2m}({p_r^2+p_{\theta}^2})+V(r)$ 27. The Hamilton's canonical equations of motion for a conservative system are$-\frac{dq_i}{dt}=\frac{\partial H}{\partial p_i}$ and $-\frac{dp_i}{dt}=\frac{\partial H}{\partial q_i}$$\frac{dq_i}{dt}=\frac{\partial H}{\partial p_i}$ and $\frac{dp_i}{dt}=\frac{\partial H}{\partial q_i}$$-\frac{dq_i}{dt}=\frac{\partial H}{\partial p_i}$ and $\frac{dp_i}{dt}=\frac{\partial H}{\partial q_i}$$\frac{dq_i}{dt}=\frac{\partial H}{\partial p_i}$ and $-\frac{dp_i}{dt}=\frac{\partial H}{\partial q_i}$ 28. The Hamilton's equations for a one-dimensional harmonic oscillator are$\dot{x}=\frac{p_x}{m}$ and $\dot{p_x}=-kx$$\dot{x}=-\frac{p_x}{m}$ and $\dot{p_x}=-kx$$\dot{x}=-\frac{p_x}{m}$ and $\dot{p_x}=kx$$\dot{x}=\frac{p_x}{m}$ and $\dot{p_x}=kx$ 29. The generalized momentum $p_x$ of a particle of mass $m$ moving with velocity $v_x$ in an electromagnetic field is$p_x=mv_x$$p_x=mv_x+qA_x$$p_x=mv_x-qA_x$$p_x=qA_xv_x$ 30. The Hamiltonian of a charged particle moving in an electromagnetic field is$H=\frac{1}{2m}(\vec{p}-q\vec{A})^2+q\phi$$H=\frac{1}{2m}(\vec{p}-q\vec{A})^2-q\phi$$H=\frac{1}{2m}(\vec{p}-q\vec{A})+q\phi$$H=\frac{1}{2m}(\vec{p}-q\vec{A})-q\phi$ Loading...
