A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to a 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m is ___________ J. (\(g=10~m/s^{2}\))

A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitude of tensions \(T_1\) and \(T_2\), respectively, are (in N) :

The amplitude of a particle executing \(SHM\) is \(3\,cm\). The displacement at which its kinetic energy will be \(25 \%\) more than the potential energy is: \(.............cm\).

Water fall from a \(40\,m\) high dam at the rate of \(9 \times 10^{4}\,kg\) per \(hour\). Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of \(100\,W\) lamps, that can be lit, is (Take \(\left.g=10\,ms ^{-2}\right)\)

Maatch Liat \(I\) List \(II\) Chose the correct answer from the options given below

A plane electromagnetic wave having a frequency \(n = 23.9\, GHz\) propagates along the positive \(z-\) direction in free space. The peak value of the electric field is \(60\, V/m\). Which among the following is the acceptable magnetic field component in the electromagnetic wave?

What is the position and nature of image formed by lens combination shown in figure? (\(f_1, f_2\) are focal lengths)

An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is \(12\,cm\). when viewed from the opposite side, the apparent distance of the bubble is observed as \(4\,cm\). If the side of the ice cube is \(24\,cm\), the refractive index of the ice cube is \(.....\).

A lamp emits monochromatic green light uniformly in all directions. The lamp is \(3\%\) efficient in converting electrical power to electromagnetic waves and consumes \(100\,W\) of power . The amplitude of the electric field associated with the electromagnetic radiation at a distance of \(5\,m\) from the lamp will be nearly.......\(V/m\)

A particle is projected at an angle of \(30^{\circ}\) from horizontal at a speed of \(60 \mathrm{~m} / \mathrm{s}\). The height traversed by the particle in the first second is \(\mathrm{h}_0\) and height traversed in the last second, before it reaches the maximum height, is \(h_1\). The ratio \(h_0: h_1\) is _________
[Take, \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) ]

A particle starts from origin at \(t=0\) with a velocity \(5 \hat{i} \mathrm{~m} / \mathrm{s}\) and moves in \(x-y\) plane under action of a force which produces a constant acceleration of \((3 \hat{i}+2 \hat{j}) \mathrm{m} / \mathrm{s}^2\). If the \(x\)-coordinate of the particle at that instant is \(84 \mathrm{~m}\), then the speed of the particle at this time is \(\sqrt{\alpha} \mathrm{m} / \mathrm{s}\). The value of \(\alpha\) is___________.

A charge of \(4.0 \mu \mathrm{C}\) is moving with a velocity of \(4.0 \times 10^6 \mathrm{~ms}^{-1}\) along the positive \(\mathrm{y}\)-axis under a magnetic field \(\vec{B}\) of strength \((2 \hat{k})\  T\). The force acting on the charge is \(x \hat{i} N\). The value of \(x\) is _______.

As per the given figure, if \(\frac{ dI }{ dt }=-1 A / s\) then the value of \(V _{ AB }\) at this instant will be \(................V\).