Consider a uniform square plate of side $$' a '$$ and mass $$'m'$$. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

An athlete in the olympic games covers a distance of $$100$$ $$m$$ in $$10$$ $$s.$$ His kinetic energy can be estimated to be in the range

A block of mass $$0.50$$ $$kg$$ is moving with a speed of $$2.00$$ $$m{s^{ - 1}}$$ on a smooth surface. It strike another mass of $$1.0$$ $$kg$$ and then they move together as a single body. The energy loss during the collision is :

Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of − 0.03 mm while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is