Physics Test - 2

The maximum kinetic energy of photootecirons is given by KE_max = h(v-v₀ ) …(i)

Where, h = Planck 's constant,

v = frequency of radiation

and v₀ = threshold frequency.

It can be seen from Eq.(i), that the maximum KE of the emitted photoelectron is proportional to the frequency of the radiation and is independent of the intensity of radiation, so it remains unchanged.

Given,F=

S=

and W = 14 J

The work done by a force in displacing a particle through a distance is given by W = F.s …(i)

Substituting the above values in Eq. (i), we get

14 =

⇒14 = -15 + 14+ 3a

⇒a = 15/3 = 5

The diffraction pattern due to a single slit is shown below

2y = 2D λ/a gives the width of central maximumD λ/a. Where, λ= wavelength of incident light.

Here, a = 2y, then from Eq.(i), we get a = 2D λ/a ⇒D = a² /2 λ.

For p number of loops in a stretched string, the length is given by l = pλ/2 …(i)

As, number of harmonics = number of loops = number of anti-nodes = p …(ii)

Also, number of nodes = number of anti-nodes + 1 Here, number of nodes = m

Number of anti-nodes = m - 1 from Eq. (ii)

p = m - 1

Putting this value of p in Eq. (i), we get

The given situation can be shown as

Let us take the moment of inertia of the system about rod R₁ then the total moment of inertia is l_T = l₁ + l₂ + l₃ …(i)

For rod R₁ , l₁ = 0

For rod R₂ , using perpendicular axis theorem, l₂ = ML² /3.

For rod R₃ , using parallel axis theorem, l₃ = l_cm + l_{(at L)} = 0 + ML² = ML²

Now, putting the values of l₁ , l₂ and l₃ in Eq. (i), we get

Applying the law of conservation of kinetic energy, KE (before collision) = KE (after collision)

⇒

Thus, the velocity of the second block after the collision is

As two pendulums begin to swing simultaneously, then n₁ T₁ = n₂ T₂ where, n₁ and n₂ are the number of oscillations of first and second pendulum respectively and T₁ and T₂ be their respective time periods.

The time period of a simple pendulum is given by

Where, I = length of the pendulum and g = acceleration due to gravity ⇒ T² ∝ l …(ii)

So. from Eqs. (i) and (i), we get

Here, n₁ = 9, n₂ = 7

⇒

Hence, the ratio of pendulum lengths l₁ :l₂ = 49.81.

Surface tension is the force applied per unit length or work done (or energy) per unit area of a liquid surface. While surface energy is the amount of work done per unit area by force.

If a force F is applied along the length L of wire for stretching by an amount x, then Young's modulus is given by

where, A = area of cross - sectional ⇒ F = (YA/L)x

The work done in stretching the wire is given by

As all the forces acting on the aircraft are balanced, so the net force on it will be zero, i.e., no external force act on it. Thus, the aircraft will keep moving with the same velocity of 150 m/s in the space.

The dimensions of force(F) = [MLT^-2 ] and density [d] = (ML^-3 T⁰ ]

From the given relation, F = y/√d

⇒ y = F√d

Substituting the above dimensions, we get [y] = [F][d]^½ = [MLT^-2 ][ML^-3 T⁰ ]^½ =[M^3/2 L^-1/2 T^-2 ]

The self or mutual inductance of a coil is the flux change due to change in current, i.e. L or M = ∅/l

So. dimensions of Mutual Inductance or Self-Inductance can be given by

⇒ [L] = [0]/[l]

Key Idea For paramagnetic substances, the magnetic susceptibility is small and positive, because they get feebly magnetised when placed in a magnetic field.

The magnetic susceptibility of a substance shows how easily a substance am be magnetised and given by x_m = I/H

where, I = intensity of magnetisation,

and H = magnetic intensity of the field

The given equation of SHM wave is y = 0.03 sin n(2t - 0.01x)m

= 0.03 sin(2πt - 0.01πx) m

Comparing it with general equation, we get y = asin(ωt-kx)

where, k = 2π/λ⇒λ = 200m

The phase deference between two particles is given by Δ∅ = kx = 2π/λ x x …(i)

Here, x = 25m

Substituting the values of x and λ in Eq. (i). we get Δ∅ = (2π/200) x 25 = (π/4)rad

The magnetic dipole moment is the product of either of pole strength and the magnetic length of dipole. Thus, it is independent of the distance of point at which it is measured. So. it remains unchanged, if the distance between point and the magnet is halved.