A child of mass \(5\,kg\) is going round a merry-goround that makes \(1\) rotation in \(3.14\,s\). The radius of the merry-go-round is \(2\,m\). The centrifugal force on the child will be \(.......\,N\)

A parallel plate capacitor having a separation between the plates \(d\) , plate area \(A\) and material with dielectric constant \(K\) has capacitance \(C_0\). Now one-third of the material is replaced by another material with dielectric constant \(2K\), so that effectively there are two capacitors one with area \(\frac{1}{3}\,A\) , dielectric constant \(2K\) and another with area \(\frac{2}{3}\,A\) and dielectric constant \(K\). If the capacitance of this new capacitor is \(C\) then \(\frac{C}{{{C_0}}}\) is

A square shaped wire with resistance of each side \(3\, \Omega\) is bent to form a complete circle. The resistance between two diametrically opposite points of the circle in unit of \(\Omega\) will be ......

A current of 5A exists in a square loop of side \(\frac{1}{\sqrt{2}} \mathrm{~m}\). Then the magnitude of the magnetic field \(B\) at the centre of the square loop will be \(p \times 10^{-6} \mathrm{~T}\). where, value of p is _____ .
\(\left[\right.\) Take \(\left.\mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\right]\).

A \(0.4\,kg\) mass takes \(8 s\) to reach ground when dropped from a certain height ' \(P\) ' above surface of earth. The loss of potential energy in the last second of fall is \(..............J\). [Take \(g =10\,m / s ^2\) ]

A train blowing a whistle of frequency \(320\,Hz\) approaches an observer standing on the platform at a speed of \(66\,m / s\). The frequency observed by the observer will be (given speed of sound \(=330\,ms ^{-1}\) ) \(.............Hz\).

The figure shows a region of length \('l'\) with a uniform magnetic field of \(0.3\, T\) in it and a proton entering the region with velocity \(4 \times 10^{5}\, ms ^{-1}\) making an angle \(60^{\circ}\) with the field. If the proton completes \(10\) revolution by the time it cross the region shown, \(l\) is close to....... \(m\) (mass of proton \(=1.67 \times 10^{-27} \,kg ,\) charge of the proton \(\left.=1.6 \times 10^{-19}\, C \right)\)

The linear mass density of a thin rod \(A B\) of length \(L\) varies from \(A\) to \(B\) as \(\lambda( x )=\lambda_{0}\left(1+\frac{ x }{ L }\right),\) where \(x\) is the distance from A. If \(M\) is the mass of the rod then its moment of inertia about an axis passing through \(A\) and perpendicular to the rod is\(......ML^{2}\)

A particle of mass \(\mathrm{m}\) is fixed to one end of a light spring having force constant \(\mathrm{k}\) and unstretched length \(\ell .\) The other end is fixed. The system is given an angular speed \(\omega\) about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is

A charged particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charged particle increases to \(4\) times its initial value. What will be the ratio of new radius to the original radius of circular path of the charged particle