A body starting at $t=0$ from origin oscillates simple harmonically with a period of 4 s . After what time will its kinetic energy by $75 \%$ of its total energy?
Three particles, each of mass $M$, situated at the vertices of an equilateral triangle of side length $l$. The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle while maintaining the original separation $l$. The initial speed that should be given to each particle is
$$ \text { Match the following. } $$
| Column-I | Column-II | ||
|---|---|---|---|
| (A) | Shear modulus | (I) | Resistance to change in volume |
| (B) | Shearing stress | (II) | Proportionality constant |
| (C) | Elastic fatigue | (III) | Tangential stress |
| (D) | Modulus of elasticity | (IV) | Temporary loss of elastic property |
| (v) | Resistance to change against deformation force | ||
The correct match is
A large storage tank, open to the atmosphere at top and filled with water, develops a small hole in its side at a point 20.0 m below the water level. If the rate of flow from the hole is $3.08 \times 10^{-5} \mathrm{~m}^3 / \mathrm{s}$, then the diameter of the hole is (take, $g=10 \mathrm{~m} / \mathrm{s}^2$ )
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