A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature \(50^{\circ} C\). The gas is now heated to double its temperature. The modified pressure is _________ Pa .

The initial pressure and volume of an ideal gas are \(P_0\) and \(V_0\). The final pressure of the gas when the gas is suddenly compressed to volume \(\frac{ V _0}{4}\) will be (Given \(\gamma=\) ratio of specific heats at constant pressure and at constant volume)

A ball projected from ground at an angle of \(45^o\) just clears a wall in front. If point of projection is \(4\,m\) from the foot of wall and ball strikes the ground at a distance of \(6\,m\) on the other side of the wall, the height of the walI is  ........ \( m\)

An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at \(30°\) and \(90°\), respectively, with respect to the horizontal axis. A third polarizer with its transmission axis at \(60°\) with the horizontal axis is placed between the two existing polarizers. The ratio of the output intensities with and without the third polarizer is ______.

A sliver wire has mass \((0.6 \pm 0.006) \; g\), radius \((0.5 \pm 0.005) \; mm\) and length \((4 \pm 0.04) \; cm\). The maximum percentage error in the measurement of its density will be \(......\,\%\)

A body of mass ' \(m\) ' is projected with a speed ' \(u\) ' making an angle of \(45^{\circ}\) with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as \(\frac{\sqrt{2} \mathrm{mu}^3}{\mathrm{Xg}}\). The value of ' \(\mathrm{X}\) ' is _______.

A coil is placed in a magnetic field \(\overrightarrow{{B}}\) as shown below: A current is induced in the coil because \(\overrightarrow{{B}}\) is:

In an \(A.C.\) circuit, the instantaneous \(e.m.f\) and current are given by. \(e=100\) \(sin\) \(20t\) \(i=20sin\) \(\left( {30t - \frac{\pi }{4}} \right)\) In one cycle of \(A.C.\), the average power consumed by the circuit and the wattless current are, respectively

When two soap bubbles of radii \(a\) and \(b ( b > a )\) coalesce, the radius of curvature of common surface is