The surface tension of soap solution is $0.035 \mathrm{N} {\mathrm{m}}^{-1}.$ The energy needed to increase the radius of the bubble from $4\mathrm{cm}$ to $6\mathrm{cm}$ is 

A wooden stick $2\mathrm{m}$ long is floating on the surface of water. The surface tension of water $0.07 \mathrm{N} {\mathrm{m}}^{-1}.$ By putting soap solution on one side of the stick, the surface tension is reduced to $0.06 \mathrm{N} {\mathrm{m}}^{-1}$. The net force on the stick will be 

A rectangular film of liquid is extended from $(4 \mathrm{cm}\times 2 \mathrm{cm})$ to $(5 \mathrm{cm}\times 4 \mathrm{cm}).$ If the work done is $3\times {10}^{-4} \mathrm{J},$ the value of the surface tension of the liquid is 

A frame made of metallic wire enclosing a surface area $A$is covered with a soap film. If the area of the frame of metallic wire. is reduced by $50\%$, the energy of the soap film will be changed by 

A liquid drop having surface energy '$E$' is spread into $512$ droplets of same size. The final surface energy of the droplets is

A big water drop is formed by the combination of 'n' small water drops of equal radii. The ratio of the surface energy of 'n' drops to the surface energy of big drop is 

$8000$ identical water drops are combined to form a big drop. Then the ratio of the final surface energy to the initial surface energy of all the drops together is

A water drop of radius $1\mathrm{cm}$ is broken into 1000 equal droplets. If the surface tension of water is $0.075 \mathrm{N} {\mathrm{m}}^{-1},$ then the gain in surface energy will be 

Work done in increasing the size of a soap bubble from a radius of $3\mathrm{cm}$ to $5\mathrm{cm}$ is nearly. (Surface tension of soap solution is $0.03{\mathrm{Nm}}^{-1}$)