The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 $$\mu $$C charge, its radius will be :
[ Take : $${1 \over {4\,\pi { \in _0}}} = $$ 9 $$ \times $$ 10⁹ N $$-$$ m²/C² ]

The maximum velocity of the photoelectrons emitted from the surface is v when light of frequency n falls on a metal surface. If the incident frequency is increased to 3n, the maximum velocity of the ejected photoelectrons will be :

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 :

The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s⁻¹ . At, t = 0 the displacement is 5 m. What is the maximum acceleration ? The initial phase is $${\pi \over 4}$$.