Match List-\(I\) with List-\(II\) Choose the correct answer from the options given below :

A wheel is rotaing freely with an angular speed \(\omega\) on a shaft. The moment of inertia of the wheel is \(I\) and the moment of inertia of the shaft is negligible. Another wheel of momet of inertia \(3I\) initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is :

By what percentage will the illumination of the lamp decrease if the current drops by \(20 \%\) ?

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

Three point charges \(q,-2 q\) and \(2 q\) are placed on \(x\)-axis at a distance \(x=0, x=\frac{3}{4} R\) and \(x=R\) respectively from origin as shown. If \(q =2 \times 10^{-6}\,C\) and \(R =2\,cm\), the magnitude of net force experienced by the charge \(-2 q\) is .......... \(N\)

In Young's double slit experiment, monochromatic light of wavelength \(5000\) \(A\) is used. The slits are \(1.0 \mathrm{~mm}\) apart and screen is placed at \(1.0 \mathrm{~m}\) away from slits. The distance from the centre of the screen where intensity becomes half of the maximum intensity for the first time is _______ \(10^{-6} \mathrm{~m}\).

The ratio of vapour densities of two gases at the same temperature is \(\frac{4}{25}\), then the ratio of r.m.s. velocities will be:

A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of \(10\, A\). The magnetic field at point \(O\) will be close to

An infinite plane sheet of charge having uniform surface charge density \(+\sigma_5 \mathrm{C} / \mathrm{m}^2\) is placed on \(\mathrm{x}-\mathrm{y}\) plane. Another infinitely long line charge having uniform linear charge density \(+\lambda_e \mathrm{C} / \mathrm{m}\) is placed at \(z=4 \mathrm{~m}\) plane and parallel to \(y\)-axis. If the magnitude values \(\left|\sigma_s\right|=2\left|\lambda_{\mathrm{e}}\right|\) then at point \((0,0,2)\), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is \(\pi \sqrt{\mathrm{n}}: 1\). The value of \(n\) is _______.

Two harmonic waves moving in the same direction superimpose to form a wave \(\mathrm{x}=\mathrm{a} \cos (1.5 \mathrm{t}) \cos (50.5 \mathrm{t})\) where \(t\) is in seconds. Find the period with which they beat (close to nearest integer)

A body \(A,\) of mass \(m=0.1\; kg\) has an initial velocity of \(3 \hat{\mathrm{i}}\; \mathrm{ms}^{-1} .\) It collides elastically with another body, \(\mathrm{B}\) of the same mass which has an initial velocity of \(5 \hat{\mathrm{j}} \;\mathrm{ms}^{-1}\). After collision. A moves with a velocity \(\overline{\mathrm{v}}=4(\hat{\mathrm{i}}+\hat{\mathrm{j}})\). The energy of \(\mathrm{B}\) after collision is written as \(\frac{\mathrm{x}}{10} \;\mathrm{J}\) The value of \(x\) is

An electric bulb rated as \(100 \mathrm{~W}-220 \mathrm{~V}\) is connected to an ac source of rms voltage 220 V. The peak value of current through the bulb is :

The maximum vertical height to which a man can throw a ball is \(136\,m\). The maximum horizontal distance upto which he can throw the same ball is \(.....\,m\)