Physics Test - 6

Given, the height of the inclined plane, h = 7m

g = 10 m/s²

By conservation of energy, Potential energy lost by the solid sphere in rolling down the inclined plane = Kinetic energy gained by the sphere.

Bedric polarisation (P) is given by

P = ?_o ?E

where, E is the electric field, and x is electric susceptibility, and it is a dimensionless quantity, Dimensional formula of P = Dimensional formula of (ε₀ ) x Dimensional formula of E

= [M^-1 L^-3 T⁴ I² ] [ML T^-3 I^-1 ] = [M⁰ L^-2 T^-1 I¹ ]

Recording to question, vectors P and Q can be written as

and

When a large bubble rises from the bottom of a water lake to its surface, then its radius becomes double.

i.e., r₂ = 2r₁

Since, volume V ∝ r³

∴ V₂ /V₁ = (r₂ /r₁ )³ = (2r₁ /r₁ )³ = 8

⇒ V₂ = 8V₁ ….(i)

From Boyle's law,

p₁ V₁ = p₂ V₂

Where, p₂ = atmospheric pressure.

p₁ V₁ = p₂ 8V₁

(from Eq. (i)J

p₂ = p₁ /8

Where. p₂ = atmospheric pressure and p₁ = pressure at depth d.

∴ p₁ = p_atmospheric + ρ gd

P₁ = p₂ + ρ gd

From Eqs. (ii) and (iii), we have

p₂ = p₂ + ?gd

7p₂ = ρ gd

7.ρgH = ρ gd

7H = d ⇒ d = 7 H

In the given circuit diagram, the galvanometer shows zero deflection, hence it is a Wheatstone ba circuit.

Hence, V_A = V_B

On replacing a new cell of emf 2E and internal resistance 3r, no effect occurs on balanced condition of bridge, i.e., V_A = V_B .

Hence, the galvanometer wil shows zero deflection.

Dimension of torque is [L² M¹ T^-2 ]

Torque = Force x Perpendicular distance

i.e., τ = F x r

∴ Dimensional formula of τ = [M L T^-2 ] [L] = [ML² T^-2 ]

Initial kinetic energy of the body,

E_i = 2π² mr²₁ f²_{1 ………..} (i)

Where, f₁ = frequency of revolution of the body.

When, r₂ = 2r₁ and f₂ = and 2f₁ , then

Change in kinetic energy,

ΔE = E_r -E_i

= 16E_i - E_i = 15 E_i

rms speed erf O₂ molecule = u

i.e …(i)

where, T = temperature and M = molecular mass. When the temperature is doubled, then O₂ dissociates into two atoms.

Hence, the atomic mass of the oxygen atom.

(M') = M/2

∴ rms velocity of the oxygen atom =

Given, terminal velocity of each small drop v₁ = 10cm/s

When 8 small drops are combined to form a bigger drop, then volume will be same.

If r₁ be radius of small drop and r₂ be the radius of biggordrop, then v₂ = v₁

∴ Terminal velocity of the drop

i.e., v ∝ r²

⇒ v₁ /v₂ = 1/4

v₂ = 4v₁ x 10 = 40 cm/s

When a body perform uniform circular motion, then centripetal force acts always in perpendicular direction to its velocity, hence work done by centripetal force is always 2ero.

Hence, work done by the centripetal force is zero, when it through (2/3)rd of the circular path.

In interference phenomenon, energy is distributed. The intensity of the resultant wave is maximum at some points and mirk mum at another point; therefore, the phenomenon of interference is based on energy conservation.

Given, magnetising field, H = 5000A/m

Magnetic flux, ϕ = 4 x 10^-5 Wb

Cross-sectional area, A = 0.4 cm² = 4 x 10^-5 m²

∴ Permeability of rod.

When a block of mass m is pulled along the smooth horizontal surface with rope erf mass m by force F , then (M + m) will be the total mass of the system.

∴ F = (M + m)a

⇒ a = F/M+m

In a sound note, various frequencies are mixed, hence beats can be produced by two sound notes only when they have nearly equal frequencies and equal amplitudes.

Total energy of simple harmonic oscillator is given by

E = (1/2) mω² A²

Where, m = mass of body performing SHM.

ω = angular velocity

and A = amplitude.

E ∝ A²