A source and a detector move away from each other in absence of wind with a speed of \(20\, {m} / {s}\) with respect to the ground. If the detector detects a frequency of \(1800\, {Hz}\) of the sound coming from the source, then the original frequency of source considering speed of sound in air \(340\, {m} / {s}\) will be \({Hz}\)

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities \(d_1\) and \(d_2\) are filled in the tube. Each liquid subtends \(90^o\) angle at centre. Radius joining their interface makes an angle \(\alpha\) with vertical. Ratio \(\frac{{{d_1}}}{{{d_2}}}\) is

Two concentric circular loops of radii \(r _{1}=30\,cm\) and \(r_{2}=50\,cm\) are placed in \(X - Y\) plane as shown in the figure. \(A\) current \(I=7\,A\) is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately.

A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point \(A\) is \(10 \mathrm{~m} / \mathrm{s}\). The ratio of its kinetic energies at point \(B\) and \(C\) is :

(Take acceleration due to gravity as \(10 \mathrm{~m} / \mathrm{s}^2\) )

Asseretion \(A:\) If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is \(5\, {mm}\) and there are \(50\) total divisions on circular scale, then least count is \(0.001\, {cm}\). Reason \(R:\) Least Count \(=\frac{\text { Pitch }}{\text { Total divisions on circular scale }}\) In the light of the above statements, choose the most appropriate answer from the options given below:

A body of mass 2 kg moving with velocity of \(\overrightarrow{\mathrm{v}}_{\mathrm{in}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}} \mathrm{ms}^{-1}\) enters into a constant force field of 6 N directed along positive z -axis. If the body remains in the field for a period of \(\frac{5}{3}\) seconds, then velocity of the body when it emerges from force field is

Intensity of sunlight is observed as \(0.092\, {Wm}^{-2}\) at a point in free space. What will be the peak value of magnetic field at that point? \(\left(\sigma_{0}=8.85 \times 10^{-12}\, {C}^{2} \,{N}^{-1} \,{m}^{-2}\right.\) )

A passenger train of length \(60\, m\) travels at a speed of \(80\, km/hr\). Another freight train of length \(120\, m\) travels at a speed of \(30\, km/hr\). The ratio of times taken by the passenger train to completely cross the freight train when: \((i)\) they are moving in the same direction, and \((ii)\) in the opposite directions is

A galvanometer ( \(G\) ) of \(2 \Omega\) resistance is connected in the given circuit. The ratio of charge stored in \(C_1\) and \(C_2\) is _______.

A proton and a deutron ( \(\mathrm{q}=+\mathrm{e}, m=2.0 \mathrm{u})\) having same kinetic energies enter a region of uniform magnetic field \(\vec{B}\), moving perpendicular to \(\vec{B}\). The ratio of the radius \(r_d\) of deutron path to the radius \(r_p\) of the proton path is _______.

Two planets have masses \(M\) and \(16\, M\) and their radii are \(a\) and \(2\, a\) respectively. The separation between the centres of the planets is \(10\, a.\) A body of mass \(m\) is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firing speed needed is

A gas mixture consists of \(3\,moles\) of oxygen and \(5\,moles\) or argon at temperature \(T.\) Considering only translational and rotational modes, the total internal  energy of the system is

The following bodies, \((1)\) a ring \((2)\) a disc \((3)\) a solid cylinder \((4)\) a solid sphere, of same mass \(m\) and radius \(R\) are allowed to roll down without slipping simultaneously from the top of the inclined plane. The body which will reach first at the bottom of the inclined plane is ........... [Mark the body as per their respective numbering given in the question]