In a metre bridge experiment the balance point is obtained if the gaps are closed by 2$$\Omega$$ and 3$$\Omega$$. A shunt of X $$\Omega$$ is added to 3$$\Omega$$ resistor to shift the balancing point by 22.5 cm. The value of X is ___________.

A point charge $$q_1=4q_0$$ is placed at origin. Another point charge $$q_2=-q_0$$ is placed at $$x=12$$ cm. Charge of proton is $$q_0$$. The proton is placed on $$x$$ axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the origin is ___________ cm.

As shown in the figure, three identical polaroids P$$_1$$, P$$_2$$ and P$$_3$$ are placed one after another. The pass axis of P$$_2$$ and P$$_3$$ are inclined at angle of 60$$^\circ$$ and 90$$^\circ$$ with respect to axis of P$$_1$$. The source S has an intensity of 256 $$\frac{W}{m^2}$$. The intensity of light at point O is ____________ $$\frac{W}{m^2}$$.

A 0.4 kg mass takes 8s to reach ground when dropped from a certain height 'P' above surface of earth. The loss of potential energy in the last second of fall is __________ J.

(Take g = 10 m/s$$^2$$)