Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature $$30 \mathrm{~cm}$$. The centre of curvature of surface is towards denser medium and a point object is placed on the principle axis in rarer medium at a distance of $$15 \mathrm{~cm}$$ from the pole of the surface. The distance of image from the pole of the surface is ____________ $$\mathrm{cm}$$.

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 series combination of resistor of resistance $$100 ~\Omega$$, inductor of inductance $$1 ~\mathrm{H}$$ and capacitor of capacitance $$6.25 ~\mu \mathrm{F}$$ is connected to an ac source. The quality factor of the circuit will be __________

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 ___________ $$\mathrm{J}$$.