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 -

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)

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 -

A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency $$\omega $$. If the radius of the bottle is 2.5 cm then $$\omega $$ is close to – (density of water = 10³ kg/m³).