A particle of mass $$0.50 \mathrm{~kg}$$ executes simple harmonic motion under force $$F=-50(\mathrm{Nm}^{-1}) x$$. The time period of oscillation is $$\frac{x}{35} s$$. The value of $$x$$ is _________.

(Given $$\pi=\frac{22}{7}$$)

At room temperature $$(27^{\circ} \mathrm{C})$$, the resistance of a heating element is $$50 \Omega$$. The temperature coefficient of the material is $$2.4 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$$. The temperature of the element, when its resistance is $$62 \Omega$$, is __________$${ }^{\circ} \mathrm{C}$$.

A straight magnetic strip has a magnetic moment of $$44 \mathrm{~Am}^2$$. If the strip is bent in a semicircular shape, its magnetic moment will be ________ $$\mathrm{Am}^2$$.

(given $$\pi=\frac{22}{7}$$)

Monochromatic light of wavelength $$500 \mathrm{~nm}$$ is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index $$=1.5$$), the central maximum is shifted to a position previously occupied by the $$4^{\text {th }}$$ bright fringe. The thickness of the glass-plate is __________ $$\mu \mathrm{m}$$.