# A particle of mass M moves in a plane under the influence of a force F = – kx directed towards the origin. What is the Lagrangian of the system in polar coordinate (r, θ)

1. $\mathbf{M\left&space;(&space;\frac{dr}{dt}&space;\right&space;)^{2}+&space;\frac{1}{2}kr^{2}}$
2. $\mathbf{M\left&space;(&space;\frac{dr}{dt}&space;\right&space;)^{2}&space;-&space;\frac{1}{2}kr^{2}}$
3. $\mathbf{\frac{1}{2}M\left&space;[&space;\left&space;(&space;\frac{dr}{dt}&space;\right&space;)^{2}&space;+&space;r^{2}\left&space;(&space;\frac{d\theta&space;}{dt}&space;\right&space;)^{2}&space;\right&space;]&space;+&space;\frac{1}{2}kr^{2}}$
4. $\mathbf{\frac{1}{2}M\left&space;[&space;\left&space;(&space;\frac{dr}{dt}&space;\right&space;)^{2}&space;+&space;r^{2}\left&space;(&space;\frac{d\theta&space;}{dt}&space;\right&space;)^{2}&space;\right&space;]&space;-&space;\frac{1}{2}kr^{2}}$

1. Positron
2. Electron
3. Neutron
4. Neutrino

# The angular momentum of the earth is about 1023 kg-m2/sec. Approximately what is the angular momentum quantum number of the earth in its orbit around the sun? (h/2π ≈ 10 joules-sec)

1. $\mathbf{10^{73}}$
2. $\mathbf{10^{50}}$
3. $\mathbf{10^{40}}$
4. $\mathbf{10^{2}}$

# Zener diode work on

1. Forward bias
2. Reverse bias
3. Zero bias
4. Infinite bias

# Disregarding the type of atoms involved, in any gas held at the same temperature. The atoms will have the same value of

1. Kinetic energy
2. Potential energy
3. Total energy
4. Velocity

1. Proton
2. Electron
3. Photon
4. Neutron

# If the length of a simple pendulum is reduced to half and mass is doubled then the time period of simple is

1. Remains unchanged
2. Halved
3. Doubled
4. Decreased by a factor of $\sqrt{2}$

# The center of mass of velocity is defined by

1. $\mathbf{V_{cm}&space;=&space;\sum&space;m_{i}&space;v_{i}}$
2. $\mathbf{V_{cm}&space;=&space;\sum&space;\frac{\mathrm{d}&space;r_{i}}{\mathrm{d}&space;t}}$
3. $\mathbf{V_{cm}&space;=&space;m_{i}\sum&space;\frac{\mathrm{d}&space;r_{i}}{\mathrm{d}&space;t}}$
4. $\mathbf{V_{cm}&space;=&space;\frac{1}{M}\sum&space;m\frac{dr_{i}}{dt}&space;}$

# A bob of mass m is moving in XY-plane as a simple pendulum. Its Lagrangian function is:

1. $\mathbf{\frac{m}{2}(\dot{\theta&space;}L)&space;-&space;mgL&space;\\sin&space;\theta}$
2. $\mathbf{\frac{m}{2}(x)&space;-&space;mgy}$
3. $\mathbf{\frac{m}{2}(\dot{\theta&space;}L)^{2}&space;-&space;mgL(1&space;-&space;cos&space;\theta)}$
4. $\mathbf{\frac{m}{2}(\dot{\theta&space;}L)^{2}&space;-&space;mgL(1&space;-&space;\\sin&space;\theta)}$