In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r₁ and r₂ . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5×10⁻⁴ s, the difference in radii, $$\left| {} \right.$$r₁ $$-$$ r₂ $$\left| {} \right.$$ is best given by :

Two wires W₁ and W₂ have the same radius r and respective densities $$\rho $$₁ and $$\rho $$₂ such that ρ₂ = 4$$\rho $$₁ . They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept under tension T. The point O is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in W₁ to W₂ is :

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer? (speed of light = 3 ×10⁸ ms^–1)

A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall. An observer, towards whom the toy car is moving, is able to hear 5 beats per second. If the velocity of sound in air is 340 m/s, the frequency of the horn of the toy car is close to :