Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be ________.

A nucleus with mass number \(184\) initially at rest emits an \(\alpha\)-particle. If the \(Q\) value of the reaction is \(5.5\, {MeV}\), calculate the kinetic energy of the \(\alpha-\) particle. (In \({MeV}\))

If \(n\) represents the actual number of deflections in a converted galvanometer of resistance \(G\) and shunt resistance \(S\). Then the total current I when its figure of merit is \(K\) will be

A piece of wood of mass \(0.03\, kg\) is dropped from the top of a \(100\, m\) height building. At the same time, a bullet of mass \(0.02\, kg\) is fired vertically upward, with a velocity \(100\, ms^{- 1}\), from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is ........ \(m\). \((g = 10\, ms^{-2})\)

A bat moving at \(10\,ms^{-1}\) towards a wall sends a sound signal of \(8000\,Hz\) towards it. On reflection it hears a sound of frequency \(f\). The value of \(f\) in \(Hz\) is close to (speed of sound \(= 320\,ms^{-1}\) )

In an experiment to determine the velocity of sound in air at room temperature using a resonance is observed when the air column has a length of \(20.0 \,cm\) for a tuning fork of frequency \(400 \,Hz\) is used. The velocity of the sound at room temperature is \(336 \,ms ^{-1}\). The third resonance is observed when the air column has a length of ......... \(cm\)

The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of \(20 \mathrm{~cm}\) from its center is \(1.5 \times 10^{-5} \  \mathrm{Tm}\). The magnetic moment of the dipole is _______ \(\mathrm{Am}^2\). (Given : \(\frac{\mu_0}{4 \pi}=10^{-7} \  \mathrm{TmA}^{-1}\) )

Two cars are approaching each other at an equal speed of \(7.2\, km / hr\). When they see each other, both blow horns having frequency of \(676\, Hz\). The beat frequency heard by each driver will be \(.....\, Hz\). [Velocity of sound in air is \(340\,m / s .]\)

The output characteristics of a transistor is shown in the figure. When \(V_{C E}\) is \(10\, V\) and \(I_{ C }=4.0\, mA ,\) then value of \(\beta_{ ac }\) is

Velocity \((v)\) and acceleration \((a)\) in two systems of units \(1\) and \(2\) are related as \(V _{2}=\frac{ n }{ m ^{2}} v _{1}\) and \(a_{2}=\frac{a_{1}}{m n}\) respectively. Here \(m\) and \(n\) are constants. The relations for distance and time in two systems respectively are