A particle of mass m moves in a potential V(x) = $$\frac{1}{2}$$ mω2x2 + $$\frac{1}{2}$$ mμv2, where x is the position coordinate, v is the speed and ω, μ are constants. The canonical momentum of the particle is

A particle of mass M moving in a straight line with speed v collides with a stationary particle of the same mass. In the centre of mass coordinate system, the first particle is deflected by 90°. The speed of second particle after collision in laboratory system will be

A

$$\frac{v}{{\sqrt 2 }}$$

B

$$\sqrt 2 v$$

C

$$v$$

D

$$\frac{v}{2}$$

Consider the following three independent cases:
i. Particle A of charge +q moves in free space with a constant velocity $$\overrightarrow {\bf{v}} $$ (v ≪ speed of light).
ii. Particle B of charge +q moves in free space in a circle of radius R with same speed v as In case i.
iii. Particle C having charge -q moves as in case ii.
If the powers radiated by A, B and C are P_A, P_B and P_C respectively then

A

P_A = 0, P_B > P_C

B

P_A = 0, P_B = P_C

C

P_A > P_B > P_C

D

P_A = P_B = P_C

The Hamiltonian of a particle is $$H = \frac{{{p^2}}}{{2m}} + pq,$$ where q is generalised coordinate and p is the corresponding canonical momentum. The Lagrangian is

A

$$\frac{m}{2}{\left( {\frac{{dq}}{{dt}} + q} \right)^2}$$

B

$$\frac{m}{2}{\left( {\frac{{dq}}{{dt}} - q} \right)^2}$$

C

$$\frac{m}{2}\left$$

D

$$\frac{m}{2}\left$$

Thermodynamic variables of a system can be volume V, pressure p, temperature T, number of particles N, internal energy E and chemical potential μ, etc. For a system to be specified by Microcanonical (MC), Canonical Ensemble (CE) and Grand Canonical (GC) ensembles, the parameters required for the respective ensembles are

A

MC : (N, V, T); CE : (E, V, N); GC : (V, T, μ)

B

MC : (E, V, N); CE : (N, V, T); GC : (V, T, μ)

C

MC : (V, T, μ); CE : (N, V, T); GC : (E, V, N)

D

MC : (E, V, N); CE : (V, T, μ): GC : (N, V, T)

What is the monoisotopic and average mass of valine? Given data: Mass of the most abundant isotope of Carbon (C°)=12.0000, Mass of most abundant isotope of Hydrogen (H°)=1.0078, Mass of most abundant isotope of Oxygen (O°)=15.9949, Mass of most abundant isotope of Nitrogen (N°)=14.0031, The average mass of Carbon (C)=12.011, The average mass of Hydrogen (H)=1.008, The average mass of Oxygen (O)=15.999, The average mass of Nitrogen (N)=14.007.

A

99.068 and 99.2361

B

99.216 and 99.326

C

99.111 and 99.321

D

99.068 and 99.132

Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction ?

A

2 9\/7 km

B

3 7\/5 km

C

1 3\/4 km

D

4 3\/8 km

A man moves 24 metres in south direction and turns 90 degrees anticlockwise and moves another 7 metres and takes a right turn and moves 3 metresand then moves 3 metres in the north direction. Find the distance between his initial and his final position.

A

25 m

B

30 m

C

27 m

D

35 m

A particle of charge q, mass m and linear momentum $$\overrightarrow {\bf{p}} $$ enters an electromagnetic field of vector potential $$\overrightarrow {\bf{A}} $$ and scalar potential $$\phi $$. The Hamiltonian of particle is

A

$$\frac{{{p^2}}}{{2m}} + q\phi + \frac{{{A^2}}}{{2m}}$$

B

$$\frac{1}{{2m}}{\left( {\overrightarrow {\bf{p}} - \frac{q}{c}\overrightarrow {\bf{A}} } \right)^2} + q\phi $$

C

$$\frac{1}{{2m}}{\left( {\overrightarrow {\bf{p}} - \frac{q}{c}\overrightarrow {\bf{A}} } \right)^2} + \overrightarrow {\bf{p}} \cdot \overrightarrow {\bf{A}} $$

D

$$\frac{{{p^2}}}{{2m}}q\phi - \overrightarrow {\bf{p}} \cdot \overrightarrow {\bf{A}} $$

A particle of charge q, mass m and linear momentum $$\overrightarrow {\bf{p}} $$ enters an electromagnetic field of vector potential $$\overrightarrow {\bf{A}} $$ and scalar potential $$\phi .$$ The Hamiltonian of the particle is

A

$$\frac{{{p^2}}}{{2m}} + q\phi + \frac{{{A^2}}}{{2m}}$$

B

$$\frac{1}{{2m}}{\left( {\overrightarrow {\bf{p}} - \frac{q}{c}\overrightarrow {\bf{A}} } \right)^2} + q\phi $$

C

$$\frac{1}{{2m}}{\left( {\overrightarrow {\bf{p}} + \frac{q}{c}\overrightarrow {\bf{A}} } \right)^2} + \overrightarrow {\bf{p}} .\overrightarrow {\bf{A}} $$

D

$$\frac{{{p^2}}}{{2m}}q\phi - \overrightarrow {\bf{p}} .\overrightarrow {\bf{A}} $$

Consider a particle of mass m moving in a one-dimensional box under the potential V = 0 for 0 ≤ x ≤ a and V = $$\infty $$ outside the box. When the particle is in its lowest energy state, the average momentum (x >) of the particle is

A

$$ = 0$$

B

$$ = \frac{h}{a}$$

C

$$ = \frac{h}{{2a}}$$

D

$$ = \frac{h}{{2\pi a}}$$

A particle of mass m moves in a potential V(x) = $$\frac{1}{2}$$ mω²x² + $$\frac{1}{2}$$ mμv², where x is the position coordinate, v is the speed and ω, μ are constants. The canonical momentum of the particle is

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