A particle with energy E is in a time independent double well potential as shown in the figure. Which, of the following statements about the particle is not correct?<br><img src="/images/question-image/engineering-physics/quantum-mechanics/1689591607-a-particle-with-energy-e-is.png" title="Quantum Mechanics mcq question image" alt="Quantum Mechanics mcq question image">

A particle of mass m is confined in an infinite potential well \[V\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {0,}&{{\text{if }}0 It is subjected to a perturbing potential $${V_P}\left( x \right) = {V_0}\sin \left( {\frac{{2\pi x}}{L}} \right)$$ within the well. Let E⁽¹⁾ and E⁽²⁾ be the corrections to the ground state energy in the first and second order in V₀.
Quantum Mechanics mcq question image

Which of the following is correct?

A

[

A. E⁽¹⁾ = 0; E⁽²⁾

B. E⁽¹⁾ > 0; E⁽²⁾ = 0

B

E⁽¹⁾ = 0; E⁽²⁾ depends on the sign of V₀

C

E⁽¹⁾ (2)

There are only three bound states for a particle of mass m in a one-dimensional potential well of the form shown in the figure. The depth V₀ of the potential satisfies
Quantum Mechanics mcq question image

A

[

A. $$\frac{{2{\pi ^2}{\hbar ^2}}}{{m{a^2}}}

B. $$\frac{{{\pi ^2}{\hbar ^2}}}{{m{a^2}}}

B

$$\frac{{2{\pi ^2}{\hbar ^2}}}{{m{a^2}}}

C

$$\frac{{2{\pi ^2}{\hbar ^2}}}{{m{a^2}}}

A particle is incident with a constant energy E on a one-dimensional potential barrier as shown in the figure.
Quantum Mechanics mcq question image

The wave functions in regions I and II are respectively

A

decaying, oscillatory

B

oscillatory, oscillatory

C

oscillatory, decaying

D

decaying, decaying

A particle of mass m is confined in the potential
Quantum Mechanics mcq question image

\[V\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{2}m{\omega ^2}{x^2},}&{{\text{for }}x Let the wave function of the particle be given by $$\psi \left( x \right) = - \frac{1}{{\sqrt 5 }}{\psi _0} + \frac{2}{{\sqrt 5 }}{\psi _1}$$
where $${\psi _0}$$ and $${\psi _1}$$ are the eigen functions of the ground state and the first excited slate respectively. The expectation value of the energy is

A

$$\frac{{31}}{{10}}\hbar \omega $$

B

$$\frac{{25}}{{10}}\hbar \omega $$

C

$$\frac{{13}}{{10}}\hbar \omega $$

D

$$\frac{{11}}{{10}}\hbar \omega $$

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 $$\frac{a}{2}.$$
Classical Mechanics mcq question image

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

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

A vertically immersed surface is shown in the below figure. The distance of its centre of pressure from the water surface is
Hydraulics and Fluid Mechanics in ME mcq question image

Hydraulics and Fluid Mechanics in ME mcq question image

A

$$\frac{{{\text{b}}{{\text{d}}^2}}}{{12}} + \overline {\text{x}} $$

B

$$\frac{{{{\text{d}}^2}}}{{12\overline {\text{x}} }} + \overline {\text{x}} $$

C

$$\frac{{{{\text{b}}^2}}}{{12}} + \overline {\text{x}} $$

D

$$\frac{{{{\text{d}}^2}}}{{12}} + \overline {\text{x}} $$

For the system of the loads shown in bellow figure, the time required for the 6.6 kg load to fall on the edge, is
Applied Mechanics and Graphic Statics mcq question image

Applied Mechanics and Graphic Statics mcq question image

A

1 sec

B

2 sec

C

3 sec

D

4 sec

The member which does not carry zero force in the structure shown in below figure, is
Applied Mechanics and Graphic Statics mcq question image

A

ED

B

DC

C

BC

D

BD

A block of mass m₁, placed on an inclined smooth plane is connected by a light string passing over a smooth pulley to mass m₂, which moves vertically downwards as shown in the below figure. The tension in the string is
Engineering Mechanics mcq question image

Engineering Mechanics mcq question image

A

$$\frac{{{{\text{m}}_1}}}{{{{\text{m}}_2}}}$$

B

$${{\text{m}}_1}{\text{g}}\sin \alpha $$

C

$$\frac{{{{\text{m}}_1}{{\text{m}}_2}}}{{{{\text{m}}_1} + {{\text{m}}_2}}}$$

D

$$\frac{{{{\text{m}}_1}{{\text{m}}_2}{\text{g}}\left( {1 + \sin \alpha } \right)}}{{{{\text{m}}_1} + {{\text{m}}_2}}}$$

A block of mass 20 kg lying on a rough horizontal plane is connected by a light string passing over a smooth pulley to another mass 5 kg, which can move freely in the Vertical direction, as shown in the below figure. The tension in the string will ___________ with the increase in coefficient of friction.
Engineering Mechanics mcq question image

A

Increase

B

Decrease

C

Not be effected

D

None of these

A particle with energy E is in a time independent double well potential as shown in the figure. Which, of the following statements about the particle is not correct?

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