The pressure wave, \(P = 0.01\,sin\,[1000t -3x]\,Nm^{-2},\) corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is \(0\,^oC.\) On some other day when temperature is \(T,\) the speed of sound produced by the same blade and at the same frequency is found to be \(336 \,ms^{-1}\). Approximate value of \(T\) is .... \(^oC\)

Identify the characteristics of an adiabatic process in a monoatomic gas.
(A) Internal energy is constant.
(B) Work done in the process is equal to the charge in internal energy.
(C) The product of temperature and volume is a constant.
(D) The product of pressure and volume is a constant.
(E) The work done to change the temperature from \(\mathrm{T}_1\) to \(\mathrm{T}_2\) is proportional to \(\left(\mathrm{T}_2-\mathrm{T}_1\right)\)
Choose the correct answer from the options given below :

A metal block of base area \(0.20\,m ^2\) is placed on a table, as shown in figure. A liquid film of thickness \(0.25\,mm\) is inserted between the block and the table. The block is pushed by a horizontal force of \(0.1\,N\) and moves with a constant speed. If the viscosity of the liquid is \(5.0 \times 10^{-3} \;Pa-s\), the speed of block is \(.........\times 10^{-3}\,m / s\)

Choose the correct option:

Find the equivalent resistance between two ends of the following circuit

A force of \(10 \; N\) acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be ...... \(N\)

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water.
(Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is \(1 \mathrm{gm} / \mathrm{cm}^3\).) The unknown mass is ________ kg.

A spring of unstretched length \(l\) has a mass \(m\) with one end fixed to a rigid support .Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity \(v\) is

In a single slit diffraction pattern, a light of wavelength \(6000\) A is used. The distance between the first and third minima in the diffraction pattern is found to be \(3 \mathrm{~mm}\) when the screen in placed 50 \(\mathrm{cm}\) away from slits. The width of the slit is _______ \(\times 10^{-4} \mathrm{~m}\).

A wooden block of mass \(5 \mathrm{~kg}\) rests on soft horizontal floor. When an iron cylinder of mass \(25\) \(\mathrm{kg}\) is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of \(0.1 \mathrm{~ms}^{-2}\). The action force of the system on the floor is equal to _______.

Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity \(K _{1}, K _{2},\) and \(K _{3}\), respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at \(100^{\circ} C\) and the ther at \(0^{\circ} C\) (see figure). If the joints of the rod are at  \(70^{\circ} C\) and \(20^{\circ} C\) in steady state and there is no loss of energy from the surface of the rod, the correct relationship between \(K _{1}, K _{2}\) and \(K _{3}\) is