A solid sphere, of radius R acquires a terminal velocity v₁ when falling (due to gravity) through a viscous fluid having a coefficient of viscosity . The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, v₂, when falling through the same fluid, the ratio (v₁/v₂) equals :

A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force F = 20 N, making an angle of 30^o with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $$\mu $$ = 0.2. The difference between the accelerations of the blocks, in case (B) and case (A) will be : (g = 10 ms^–2)

One kg of water, at 20^oC, heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of 20 $$\Omega $$. The rms voltage in the mains is 200 V. Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to : [Specific heat of water = 4200 J/(kg ^oC), Latent heat of water = 2260 kJ/kg]

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, $${{{\lambda _1}} \over {{\lambda _2}}}$$, of the photons emitted in this process is :