A carpet of mass ' $M$ ' made of a material is rolled along its length in the form of a cylinder of radius ' $R$ ' and kept above the rough floor. If the carpet is unrolled without sliding to a radius ' $R / 2$ '. The change in potential energy is ( $\mathrm{g}=$ acceleration due to gravity)

A water film is formed between two parallel wires of 10 cm length. The distance of 0.5 cm between the wires is increased by 1 mm . The work done in the process is (surface tension of water $=72 \mathrm{~N} / \mathrm{m}$)

A coil of self inductance L is connected in series with a bulb B and an a.c. source. Brightness of the bulb decreases when

A transverse wave travelling along a stretched string has a speed of $30 \mathrm{~m} / \mathrm{s}$ and a frequency of 250 Hz . The phase difference between two points on the string 10 cm apart at the same instant is