A block of a mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is $$\frac{\pi}{\sqrt x}$$ in SI unit. The value of $$x$$ is ____________.

Vectors $$a\widehat i + b\widehat j + \widehat k$$ and $$2\widehat i - 3\widehat j + 4\widehat k$$ are perpendicular to each other when $$3a + 2b = 7$$, the ratio of $$a$$ to $$b$$ is $${x \over 2}$$. The value of $$x$$ is ____________.

A hole is drilled in a metal sheet. At $$\mathrm{27^\circ C}$$, the diameter of hole is 5 cm. When the sheet is heated to $$\mathrm{177^\circ C}$$, the change in the diameter of hole is $$\mathrm{d\times10^{-3}}$$ cm. The value of d will be __________ if coefficient of linear expansion of the metal is $$1.6\times10^{-5}/^\circ$$C.

Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be $$\sqrt x$$ cm. The value of $$x$$ is ________.