1.

A cylinder-piston system contains N atoms of an ideal gas. If 𝑡_𝑎𝑣𝑔 is the average time between successive collisions of a given atom with other atoms. If the temperature T of the gas is increased isobarically, then 𝑡_𝑎𝑣𝑔 is proportional to :

• \(\sqrt{T}\)
• \(\frac{1}{\sqrt{T}}\)
• T
• \(\frac{1}{T}\)

2.

A one-dimensional infinite square-well potential is given by:
\(v(x)=0\,\,for\,\,-\frac{a}{2}<x<+\frac{a}{2}\)= ∞ elsewhere
Let 𝐸_𝑒 (𝑥) and ψ_𝑒 (𝑥) be the ground state energy and the corresponding wave function, respectively, if an electron (e) is trapped in that well. Similarly, let 𝐸_µ(𝑥) and ψ_µ (𝑥) be the corresponding quantities, if a muon (µ) is trapped in the well. Choose the correct option:

3.

Given that the rest mass of electron is 0.511MeV/c ² , the speed (in units of c) of an electron with kinetic energy 5.11MeV is closest to:

• 0.996
• 0.993
• 0.990
• 0.998

4.

A 15.7mW laser beam has a diameter of 4mm. If the amplitude of the associated magnetic field is expressed as \(\frac{𝐴}{\sqrt{ε_0𝑐^3}}\) , the value of A is: (𝜀₀ is the free space permittivity and 𝑐 is the speed of light)

• 50
• 35.4
• 100
• 70.8

5.

A ball is dropped from a height ℎ to the ground. If the coefficient of restitution is 𝑒, the time required for the ball to stop bouncing is proportional to:

• \(\frac{2+e}{1-e}\)
• \(\frac{1+e}{1-e}\)
• \(\frac{1-e}{1+e}\)
• \(\frac{2-e}{1+e}\)

6.

If the electric field of an electromagnetic wave is given by,
𝐸⃗ = (4𝑥̂ + 3𝑦̂)𝑒 ^{𝑖(𝜔𝑡+𝑎𝑥−600𝑦)} 
then the value of a is: (all values are in the SI units)

• 450
• --450
• 800
• −800