A sealed flask with a capacity of $2\, dm ^3$ contains $11 \, g$ of propane gas The flask is so weak that it will burst if the pressure becomes $2\, MPa$ The minimum temperature at which the flask will burst is ______${ }^{\circ} C$ [Nearest integer]
(Given: $R =8.3 \,J \,K ^{-1} mol ^{-1}$ Atomic masses of $C$ and $H$ are $12\, u$ and $1 \,u$ respectively) (Assume that propane behaves as an ideal gas)
A bob of mass \(m\) is suspended at a point \(O\) by a light string of length \(l\) and left to perform vertical motion (circular) as shown in the figure. Initially, by applying horizontal velocity \(v_0\) at the point ‘A’, the string becomes slack when the bob reaches at the point ‘D’. The ratio of the kinetic energy of the bob at the points B and C is:
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is:
The matter is made up of very tiny particles and these particles are so small that we cannot see them with naked eyes.
The three states of matter are as follows: