A person standing on a spring balance inside a stationary lift measures \(60 \,kg\). The weight of that person if the lift descends with uniform downward acceleration of \(1.8\, m / s ^{2}\) will be \(_{-} N\). \(\left[ g =10\, m / s ^{2}\right]\)

Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis \(A B\) as shown in figure is \(\sqrt{\frac{8}{x}}\). The value of \(x\) is _______.

Two objects are projected with same velocity ' \(u\) ' however at different angles \(\alpha\) and \(\beta\) with the horizontal. If \(\alpha+\beta=90^{\circ}\), the ratio of horizontal range of the first object to the \(2^{\text {nd }}\) object will be :

Electric potential at a point \(P\) due to a point charge of \(5 \times 10^{-9}\; C\) is \(50 \;V\). The distance of \(P\) from the point charge is ......... \(cm\) (Assume, \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^{+9}\; Nm ^2 C ^{-2}\))

A simple pendulum with length \(100\,cm\) and bob of mass \(250\,g\) is executing S.H.M. of amplitude \(10\,cm\). The maximum tension in the string is found to be \(\frac{x}{40}\,N\). The value of \(x\) is \(..........\).

For an experimental expression \(y=\frac{32.3 \times 1125}{27.4}\), where all the digits are significant. Then to report the value of \(y\) we should write

An inductor of \(0.5 \,mH\), a capacitor of \(200 \,\mu F\) and a resistor of \(2 \,\Omega\) are connected in series with a \(220 \,V\) ac source. If the current is in phase with the emf, the frequency of ac source will be ................ \(\times 10^{2} \,Hz\)

A hydrogen atom changes its state from \(n=3\) to \(\mathrm{n}=2\). Due to recoil, the percentage change in the wave length of emitted light is approximately \(1 \times 10^{-\mathrm{n}}\). The value of \(\mathrm{n}\) is _______. [Given \(\mathrm{Rhc}=13.6 \mathrm{eV}, \mathrm{hc}=1242 \mathrm{eV} \mathrm{nm}\), \(\mathrm{h}=6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s}\), mass of the hydrogen atom \(\left.=1.6 \times 10^{-27} \mathrm{~kg}\right]\)

Three solid spheres each of mass \(\mathrm{m}\) and diameter \(d\) are stuck together such that the lines connecting the centres form an equilateral triangle of side of length \(d\). The ratio \(\mathrm{I}_{0} / \mathrm{I}_{\mathrm{A}}\) of moment of inertia \(\mathrm{I}_{0}\) of the system about an axis passing the centroid and about center of any of the spheres \(\mathrm{I}_{\mathrm{A}}\) and perpendicular to the plane of the triangle is

Find the bindng energy per nucleon for \(\frac{50}{120}\, Sn\). Mass of proton \(m _{ P }=1.00783\, U ,\) mass of \(m _{ n }=1.00867\, U\) and \(mass\) of tin nucleus \(m _{ Sn }=119.902199\) \(U.\)\(......MeV\) (take \(1 U =931\, MeV )\)

When a rubber ball is taken to a depth of \(......\,{m}\) in deep sea, its volume decreases by \(0.5\, \%\) (The bulk modulus of rubber \(=9.8 \times 10^{8}\, {Nm}^{-2}\) Density of sea water \(=10^{3} {kgm}^{-3}\) \(\left.{g}=9.8\, {m} / {s}^{2}\right)\)

The ratio of the coefficient of volume expansion of a glass container to that of a viscous liquid kept inside the container is \(1 : 4\). What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures ?