A plano-convex lens (focal length f₂, refractive index $$\mu $$₂, radius of curvature R) fits exactly into a plano-concave lens (focal length f₁, refractive index $$\mu $$₁, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be :

Two particles A, B are moving on two concentric circles of radii R₁ and R₂ with equal angular speed $$\omega $$. At t = 0, their positions and direction of motion are shown in the figure. :



The relative velocity $${\overrightarrow V _A} - {\overrightarrow V _B}$$ at t = $${\pi \over {2\omega }}$$ is given by :

A soap bubble, blown by a mechanical pump at the mouth of a tube, increases in volume, with time, at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by :

A simple harmonic motion is represented by :

y = 5 (sin 3 $$\pi $$ t + $$\sqrt 3 $$ cos 3 $$\pi $$t) cm

The amplitude and time period of the motion are :