A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be _________ cm.

A body of mass $$5 \mathrm{~kg}$$ is moving with a momentum of $$10 \mathrm{~kg} \mathrm{~ms}^{-1}$$. Now a force of $$2 \mathrm{~N}$$ acts on the body in the direction of its motion for $$5 \mathrm{~s}$$. The increase in the Kinetic energy of the body is ___________ $$\mathrm{J}$$.

The ratio of wavelength of spectral lines $$\mathrm{H}_{\alpha}$$ and $$\mathrm{H}_{\beta}$$ in the Balmer series is $$\frac{x}{20}$$. The value of $$x$$ is _________.

A steel rod of length $$1 \mathrm{~m}$$ and cross sectional area $$10^{-4} \mathrm{~m}^{2}$$ is heated from $$0^{\circ} \mathrm{C}$$ to $$200^{\circ} \mathrm{C}$$ without being allowed to extend or bend. The compressive tension produced in the rod is ___________ $$\times 10^{4} \mathrm{~N}$$. (Given Young's modulus of steel $$=2 \times 10^{11} \mathrm{Nm}^{-2}$$, coefficient of linear expansion $$=10^{-5} \mathrm{~K}^{-1}$$ )