A convex lens of focal length $$\mathrm{T}$$ is used to form an image whose size is one fourth that of size of the object. Then the object distance is

A particle at rest starts moving with a constant angular acceleration of $$4 \mathrm{~rad} / \mathrm{s}^2$$ in a circular path. At what time the magnitude of its centripetal acceleration and tangential acceleration will be equal?

A metal conductor of length $$1 \mathrm{~m}$$ rotates vertically about one of its ends at an angular velocity of $$5 \mathrm{~rad} / \mathrm{s}$$. If horizontal component of earth's magnetic field is $$0.2 \times 10^{-4} \mathrm{~T}$$, then the e.m.f. developed between the two ends of the conductor is

A black rectangular surface of area '$$\mathrm{A}$$' emits energy '$$\mathrm{E}$$' per second at $$27^{\circ} \mathrm{C}$$. If length and breadth is reduced to $$(1 / 3)^{\text {rd }}$$ of its initial value and temperature is raised to $$327^{\circ} \mathrm{C}$$ then energy emitted per second becomes