There is a small hole in a hollow sphere. Water enters it when it is taken to a depth of $40 \, cm$ under water. The surface tension of water is $0.07 \, N/m$. The diameter of the hole is ...... $mm$.

Two satellites of earth,$S_1$ and $S_2$ are moving in the same orbit. The mass of $S_1$ is four times the mass of $S_2.$ Which one of the following statements is true?

The conditions under which transpiration would be most rapid are:

Which of the following compounds is the least ionic?

Let $a, b, c$ be non-zero real numbers such that $\int_{0}^{1} (1 + \cos^8 x)(ax^2 + bx + c) dx = \int_{0}^{2} (1 + \cos^8 x)(ax^2 + bx + c) dx$. Then the quadratic equation $ax^2 + bx + c = 0$ has:

In the given figure,a ring of mass $m$ is kept on a horizontal surface,while a body of equal mass $m$ is attached through a string wound on the ring. When the system is released,the ring rolls without slipping. Consider the following statements and choose the correct option.
$(i)$ Acceleration of the centre of mass of the ring is $g/3$.
$(ii)$ Acceleration of the hanging particle is $2g/3$.
$(iii)$ Frictional force (on the ring) acts along the forward direction.
$(iv)$ Frictional force (on the ring) acts along the backward direction.