The frequency ($$\nu$$) of an oscillating liquid drop may depend upon radius ($$r$$) of the drop, density ($$\rho$$) of liquid and the surface tension (s) of the liquid as $$\nu=r^a\rho^b s^c$$. The values of a, b and c respectively are

If two vectors $$\overrightarrow P = \widehat i + 2m\widehat j + m\widehat k$$ and $$\overrightarrow Q = 4\widehat i - 2\widehat j + m\widehat k$$ are perpendicular to each other. Then, the value of m will be :

A body of mass 200g is tied to a spring of spring constant 12.5 N/m, while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed 5 rad/s. Then the ratio of extension in the spring to its natural length will be :

A convex lens of refractive index 1.5 and focal length 18cm in air is immersed in water. The change in focal length of the lens will be ___________ cm.

(Given refractive index of water $$=\frac{4}{3}$$)