Two ions having same mass have charges in the ratio \(1: 2\). They are projected normally in a uniform magnetic field with their speeds in the ratio \(2: 3\). The ratio of the radii of their circular trajectories is -

Given below are two statements: one is labelled as Assertion\((A)\) and the other is labelled as Reason \((R).\) \(Assertion\) \((A)\) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading. \(Reason\) \((R)\) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling. In the light of the above statements, choose the correct answer from the options given below :

In a compound microscope the focal length of objective lens is \(1.2\, cm\) and focal length of eye piece is \(3.0\, cm\). When object is kept at \(1.25\, cm\) in front of objective, final image is formed at infinity. Magnifying power of the compound microscope should be

Three identical coils \(C _1, C _2\) and \(C _3\) are closely placed such that they share a common axis.\(C _2\) is exactly midway.\(C _1\) carries current I in anti-clockwise direction while \(C _3\) carries current I in clockwise direction. An induced current flows through \(C _2\), will be in clockwise direction when

Two light waves of wavelengths \(800\) and \(600\,nm\) are used in Young's double slit experiment to obtain interference fringes on a screen placed \(7\,m\) away from plane of slits. If the two slits are separated by \(0.35\,mm\), then shortest distance from the central bright maximum to the point where the bright fringes of the two wavelength coincide will be \(.............mm\).

A fighter jet is flying horizontally at a certain altitude with a speed of \(200 \; ms ^{-1}\). When it passes directly overhead an anti-aircraft gun, bullet is fired from the gun, at an angle \(\theta\) with the horizontal, to hit the jet. If the bullet speed is \(400 \; m / s\), the value of \(\theta\) will be \(\dots \; {}^o\)

Water drops are falling from a nozzle of a shower onto the floor, from a height of \(9.8\, {m}\). The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor.  (In \(m\))

An electron of mass ' m ' with an initial velocity \(\overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{i}\left(\mathrm{v}_0\gt0\right)\) enters an electric field \(\overrightarrow{\mathrm{E}}=-\mathrm{E}_{\mathrm{o}} \hat{\mathrm{k}}\). If the initial de Broglie wavelength is \(\lambda_0\), the value after time t would be _______.

A prism of angle \(75^{\circ}\) and refractive index \(\sqrt{3}\) is coated with thin film of refractive index 1.5 only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be ___________ .
\(\left(\sin 15^{\circ}=0.25\right.\) and \(\left.\sin 25^{\circ}=0.43\right)\)

A steel rod has a radius of \(20\,mm\) and a length of \(2.0\,m\). A force of \(62.8\,kN\) stretches it along its length. Young's modulus of steel is \(2.0 \times 10^{11}\,N / m ^2\). The longitudinal strain produced in the wire is \(..........\times 10^{-5}\)