A calorimeter of water equivalent \(20\, g\) contains \(180\, g\) of water at \(25^{\circ} C\). '\(m\)' grams of steam at \(100^{\circ} C\) is mixed in it till the temperature of the mixure is \(31^{\circ} C\). The value of \('m'\) is close to (Latent heat of water \(=540\) cal \(g ^{-1}\), specific heat of water \(=1\) cal \(g^{-1}{ }^{\circ} C ^{-1}\) )

In a spring gun having spring constant \(100\, {N} / {m}\) a small ball \('B'\) of mass \(100\, {g}\) is put in its barrel (as shown in figure) by compressing the spring through \(0.05\, {m}\). There should be a box placed at a distance \('d'\) on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of \(2\, {m}\) above the ground. The value of \(d\) is \(....{m} .\) \(\left(g=10\, {m} / {s}^{2}\right)\)

A shunt of resistance \(1\,\Omega \) is connected across a galvanometer of \(120\,\Omega \) resistance. A current of \(5.5\, ampere\) gives full scale deflection in the galvanometer. The current that will give full scale deflection in the absence of the shunt is nearly ............... \(ampere\)

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is \(20 \,cm\). The length of the open organ pipe is........\(cm\).

Calculate the limit of resolution of a telescope objective having a diameter of \(200\, cm\), if it has to detect light of wavelength \(500\, nm\) coming from a star

A nucleus of masss \(M\) emits \(\gamma\)-ray photon of frequency \('v'.\) The loss of internal energy by the nucleus is:

A wire having a linear mass density \(9.0 \times 10^{-4} \;{kg} / {m}\) is stretched between two rigid supports with a tension of \(900\; {N}\). The wire resonates at a frequency of \(500\;{Hz}\). The next higher frequency at which the same wire resonates is \(550\; {Hz}\). The length of the wire is \(...... {m}\)

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly _______.

Consider a badminton racket with length scales as shown in the figure.If the mass of the linear and circular portions of the badminton racket are same \((M)\) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, \(\frac{r}{2}\) distance from the end \(A\) of the handle will be ....... \(Mr^2\)?

Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth \(d=\frac{R}{2}\) from the surface of earth, if its werght on the surface of earth is \(200\,N\), will be \(...........\,N\) ( \(Given R =\) Radrus of earth)

A point dipole \(\vec p =  - {p_0}\hat x\) is kept at the origin. The potential and electric field due to this dipole on the \(y-\) axis at a distance \(d\) are, respectively : (Take \(V = 0\) at infinity)

The moment of inertia of a uniform cylinder of length \(l\) and radius \(R\) about its perpendicular bisector is \(I\). What is the ratio \(l/R\) such that the moment of inertia is minimum?