In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by $$0.5 \mathrm{~mm}$$ on a complete rotation of the circular scale. The zero of circular scale lies 6 divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, 4 linear scale divisions are clearly visible while $$46^{\text {th }}$$ division the circular scale coincide with the reference line. The diameter of the wire is ______________ $$\times 10^{-2} \mathrm{~mm}$$.

In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of $$0.5 \mathrm{~s}$$ is measured from time of 100 oscillation with a watch of $$1 \mathrm{~s}$$ resolution. If measured value of length is $$10 \mathrm{~cm}$$ known to $$1 \mathrm{~mm}$$ accuracy, The accuracy in the determination of $$\mathrm{g}$$ is found to be $$x \%$$. The value of $$x$$ is ___________.

The one division of main scale of Vernier callipers reads $$1 \mathrm{~mm}$$ and 10 divisions of Vernier scale is equal to the 9 divisions on main scale. When the two jaws of the instrument touch each other, the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between $$4.1 \mathrm{~cm}$$ and $$4.2 \mathrm{~cm}$$ and $$6^{\text {th }}$$ Vernier division coincides scale division. The diameter of the bob will be ____________ $$\times$$ 10^$$-$$2 cm.

The Vernier constant of Vernier callipers is 0.1 mm and it has zero error of ($$-$$0.05) cm. While measuring diameter of a sphere, the main scale reading is 1.7 cm and coinciding vernier division is 5. The corrected diameter will be _________ $$\times$$ 10^$$-$$2 cm.