A particle of mass 250 g executes a simple harmonic motion under a periodic force $$\mathrm{F}=(-25~x)\mathrm{N}$$. The particle attains a maximum speed of 4 m/s during its oscillation. The amplitude of the motion is ___________ cm.

A metal block of base area 0.20 m$$^2$$ is placed on a table, as shown in figure. A liquid film of thickness 0.25 mm is inserted between the block and the table. The block is pushed by a horizontal force of 0.1 N and moves with a constant speed. IF the viscosity of the liquid is $$5.0\times10^{-3}~\mathrm{Pl}$$, the speed of block is ____________ $$\times10^{-3}$$ m/s.

A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of 54 km/hr is $$t(1-e^{-\pi/2})s$$. The value of t is ____________.

Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are 2.8 (medium $$-1$$) and 6.8 (medium $$-2$$), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be $${\tan ^{ - 1}}{\left( {1 + {{10} \over \theta }} \right)^{{1 \over 2}}}$$ the value of $$\theta$$ is __________.

(Given for dielectric media, $$\mu_r=1$$)