The mean free path of molecules of a certain gas at \(STP\) is \(1500\,d\), where \(d\) is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at \(373\,K\) is approximately \(..........\,d\)

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is _______. (Given \(=\) Radius of geo-stationary orbit for earth is \(4.2 \times 10^4 \mathrm{~km}\) )

Two masses \(A\) and \(B ,\) each of mass \(M\) are fixed together by a massless spring. \(A\) force acts on the mass \(B\) as shown in figure. If the mass \(A\) starts moving away from mass \(B\) with acceleration \('a',\) then the acceleration of mass \(B\) wil be :-

A bead of mass ' \(m\) ' slides without friction on the wall of a vertical circular hoop of radius ' \(R\) ' as shown in figure. The bead moves under the combined action of gravity and a massless spring ( k ) attached to the bottom of the hoop. The equilibrium length of the spring is ' \(R\) '. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ' R ', would be (spring constant is ' k ', g is accleration due to gravity)

in circular plate of mass \(M\) and radius \(R\) has its density varying as \(p\left( r \right) = {p_0}\,r\) with \(P_0\) as constant and \(r\) is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is \(I = aMR^2\) . The value of the coefficient \(a\) is

The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is

The reading of the ammeter for a silicon diode in the given circuit is.......\(mA\)

An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as \(100\) Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by \(30^{\circ}\) in clockwise direction, the intensity of emerging light will be .......... Lumens.

When radiation of wavelength \(\lambda \) is incident on a metallic surface, the stopping potential is \(4.8\) volts. If the same surface is illuminated with radiation of double the wavelength, then the stopping potential becomes \(1.6\) volts. Then the threshold wavelength for the surface is

Energy released when two deuterons \(\left({ }_1 \mathrm{H}^2\right)\) fuse to form a helium nucleus \(\left({ }_2 \mathrm{He}^4\right)\) is :
(Given : Binding energy per nucleon of \({ }_1 \mathrm{H}^2=1.1 \mathrm{MeV}\) and binding energy per nucleon of \({ }_2 \mathrm{He}^4=7.0 \mathrm{MeV}\))

A uniform sphere of weight \(W\) and radius \(5\, cm\) is being held by a string as shown in the figure. The tension in the string will be

Radiation coming from transition \(n = 2\) to \(n = 1\) of hydrogen atoms fall of \(He^+\) ions in \(n = 1\) and \(n = 2\) states. The possible. Transition of helium ions as they absorb energy from the radiation is