Physics Test 159

During a rainy day, rain is falling vertically down with a velocity 2 m/s. A boy at rest starts his motion with a constant acceleration of 2 m/s² along a straight road. Find the rate at which the angle of the axis of the umbrella with vertical should be changed so that the rain always appears to fall parallel to the axis of the umbrella.

A resistance of 2 Ω is connected across one gap of a metre-bridge and unknown resistance, greater than 2Ω, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm, neglecting any end correction, the unknown resistance is

A cobalt (atomic no. = 27) target is bombarded with electrons and the wavelengths of its characteristic X-rays spectrum are measured. A second weak characteristic spectrum is also found due to an impurity in the target. The wavelength of the K_α lines are 225.0 pm (cobalt) and 100.0 pm (impurity). Atomic number of the impurity is

A circular conducting loop of radius r₀ and having resistance λ per unit length as shown in the figure is placed in a magnetic field B which is constant. The ends of the loop are crossed and pulled in opposite directions with a velocity v such that the loop always remains circular and the radius of the loop goes on decreasing, then

When a particle of mass m is suspended vertically by a spring of unstretched length 'a', the spring is stretched to a total length ℓ. The particle is pulled down by a small distance 'b' from equilibrium position and then released. The angular frequency of the simple harmonic motion executed by the particle is

In YDSE, let A and B be two slits as shown. Thin films of thickness t_A and t_B and refractive indices μ_A and μ_B are placed in front of A and B respectively. If μ_At_A = μ_Bt_B, then the central maxima will

A sound source S and observer O₁ and O₂ are placed as shown in figure. S is always at rest and O₁ and O₂ start moving along positive y–axis and positive x-axis respectively with the same constant speed v₀ at t = 0 away from S. At t = 5 sec, f₁ and f₂ represent apparent frequencies of sound received by O₁ and O₂ respectively. Then the ratio  (f₁/f₂) is

A cubical block of side 'a' and density 'ρ' slides down a fixed inclined plane of inclination θ = 37° with a constant velocity v as shown. There is a thin film of viscous liquid of thickness t between the inclined plane and the block. Then the coefficient of viscosity of the liquid will be

A diverging lens of focal length f₁ is placed infront of and coaxially with a concave mirror of focal length f₂. The separation between the lens and the mirror is d. A parallel beam of light incident on the lens returns as a parallel beam from the arrangement.

A parallel plate capacitor with initial plate distance d₀ is charged upto voltage V₀ and then detached from the charger. Now the distance between the plates is varied periodically according to the law d = d₀ + d₁ sinωt. The value of d₁ if the potential difference across the capacitor changes according to the law V =  is