Two spheres P and Q for equal radii have densities $$\rho$$₁ and $$\rho$$₂, respectively. The spheres are connected by a massless string and placed in liquids L₁ and L₂ of densities $$\sigma$$₁ and $$\sigma$$₂ and viscosities $${\eta _1}$$ and $${\eta _2}$$, respectively. They float in equilibrium with the sphere P in L₁ and sphere Q in L₂ and the string being taut (see figure) If sphere P along in L₂ has terminal velocity v_P and Q alone in L₁ ha terminal velocity v_Q, then

Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the temperature of 0.5 kg water by 40 K. This heater is replaced by a new heater having two wires of the same material, each of length L and diameter 2d. The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by 40 K?

A solid sphere of radius R and density $$\rho $$ is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3$$\rho $$. The complete arrangement is placed in a liquid of density 2$$\rho $$ and is allowed to reach equilibrium. The correct statement(s) is (are)