A conducting ring of certain resistance is falling towards a current carrying straight long conductor. The ring and conductor are in the same plane. Then

Moving coil galvanometers \(\mathrm{M}_{1}\) and \(\mathrm{M}_{2}\) have resistance, number of turns, area of coil and magnetic field as follows.
\(\mathrm{R}_{1}=10 \Omega, \mathrm{R}_{2}=14 \Omega, \mathrm{N}_{1}=30, \mathrm{~N}_{2}=42\)
\(\mathrm{A}_{1}=3 \cdot 6 \times 10^{-3} \mathrm{~m}^{2}, \mathrm{~A}_{2}=1 \cdot 8 \times 10^{-2} \mathrm{~m}^{2},\) \(\mathrm{~B}_{1}=0 \cdot 25 \mathrm{~T}, \mathrm{~B}_{2}=0 \cdot 50 \mathrm{~T}\)
(Spring constants are same for both materials)
The ratio of (i) current sensitivity and (ii) voltage sensitivity for galvanometer
\(\left(\mathrm{M}_{2}\right.\) to \(\left.\mathrm{M}_{1}\right)\) is respectively

An ideal gas has pressure $P$, volume $V$ and absolute temperature $T$. If $m$ is the mass of each molecule and $K$ is the Boltzmann constant then density of the gas is

The total charge induced in a conducting loop when it is moved in a uniform magnetic field depends on

The fundamental frequency of air column in pipe 'A' closed at one end is in unison with second overtone of an air column in pipe 'B' open at both ends. The ratio of length of air column in pipe 'A' to that of air column in pipe ' \(\mathrm{B}\) ' is

If the radius of a planet is 'R' and density ' \(\varrho\) ', then the escape velocity 'Ve' of any body from its surface will be proportional to

A particle of mass \(m\) is projected with velocity \(v\) making an angle of \(45^{\circ}\) with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be

Which of the following compounds do not give different isomers on monochlorination?

Which among the following statements is true for haloalkyne?

For a process, entropy change of a system is expressed as

The equation of tangents to the circle \(x^2+y^2=4\) which are parallel to \(x+2 y+3=0\) are

The angular displacement of body performing circular motion is given by \(\theta=5 \sin \frac{\pi t}{6}\). The angular velocity of the body at \(t=3\) second will be \(\left[\sin \frac{\pi}{2}=1, \cos \frac{\pi}{2}=0\right]\)

A ring and a disc roll on the horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is 4 J then total kinetic energy of the disc is