KEAM 2018

A solid sphere of volume $\mathrm{V}$ experiences a viscous force $\mathrm{F}$ when descending with a speed $\mathrm{v}$ in a liquid. If another solid sphere of volume $27 \mathrm{V}$ descends with the same speed $\mathrm{v}$ in the same liquid, it experiences a viscous force

A boy formed a bubble and a liquid drop form the same soapy water. The pressure difference between inside and outside of the soap bubble is measured to be $100 \mathrm{N}/{\mathrm{m}}^2.$ If the radius of the droplet is half of the radius of the bubble, then the pressure difference between the inside and outside of the droplet is

Two soap bubbles of radii $3 \mathrm{mm}$ and $4\mathrm{ }\mathrm{mm}$ confined in vacuum coalesce isothermally to form a new bubble. The radius of the bubble formed $\left(\mathrm{in}\mathrm{ }\mathrm{mm}\right)$ is

A soap bubble of radius $r$ is blown up to form a bubble of radius $2r$ under isothermal conditions. If $\sigma$ is the surface tension of the soap solution, the energy spent in the process is