The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea (7.8 mm). This surface separateds two media of refractive indices 1 and 1.34. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus -

An unknown metal of mass 192 g heated to a temperature of 100^oC was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of 8.4^oC. Calculate the specific heat of the unknown metal if water temperature stabilizes at 21.5^oC. (Specific heat of brass is 394 J kg^–1 K^–1)

A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is -

A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between the plates. The work done by the capacitor on the slab is :