A free neutron decays into a proton but a free proton does not decay into neutron. This is because

A galvanometer having a coil resistance \(100 \;\Omega\) gives a full scale deflection when a current of \(1 \;\mathrm{mA}\) is passed through it. What is the value of the resistance which can convert this galvanometer into a voltmeter giving full scale deflection for a potential difference of \(10\; \mathrm{V} ?\)......\(k\Omega\)

Two identical thin biconvex lenses of focal length \(15\, cm\) and refractive index \(1.5\) are in contact with each other. The space between the lenses is filled with a liquid of refractive index \(1.25\). The focal length of the combination is \(cm\).

The escape velocity of a body on a planet  \('A'\)  is \(12 \,kms ^{-1}\). The escape velocity of the body on another planet  \('B'\) , whose density is four times and radius is half of the planet  \('A'\), is ................... \(kms ^{-1}\)

Distance of the centre of mass of a solid uniform cone from its vertex is \(z_0\) . If the radius of its base is \(R\) and its height is \(h\) then \(z_0\) is equal to

The disc of mass \(M\) with uniform surface mass density \(\sigma\) is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position \(\frac{x}{3} \frac{a}{\pi}, \frac{x}{3} \frac{a}{\pi}\) where \(x\) is ....... . (Round off to the Nearest Integer) \([ a\) is an area as shown in the figure \(]\)

According to Bohr's theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the \(n^{th}\) orbit is proportional to (\(n =\) principal quantum number)

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is ___________. \((\pi=3.14)\)

A particle of mass \('{m}'\) is moving in time \('t'\) on a trajectory given by \(\overrightarrow{{r}}=10 \alpha {t}^{2}\, \hat{{i}}+5 \beta({t}-5)\, \hat{{j}}\) Where \(\alpha\) and \(\beta\) are dimensional constants. The angular momentum of the particle becomes the same as it was for \({t}=0\) at time \({t}=\) .....\(seconds.\)

An expression for a dimensionless quantity \(P\) is given by \(P=\frac{\alpha}{\beta} \log _{e}\left(\frac{ kt }{\beta x }\right)\); where \(\alpha\) and \(\beta\) are constants, \(x\) is distance ; \(k\) is Boltzmann constant and \(t\) is the temperature. Then the dimensions of \(\alpha\) will be

Consider a cylinder of mass \(M\) resting on a rough horizontal rug that is pulled out from under it with acceleration \('a'\) perpendicular to the axis of the cylinder. What is \(F_{friction}\) at point \(P\) ? It is assumed that the cylinder does not slip

Water from a tap emerges vertically downwards with an initial speed of \(1.0\,ms^{-1}.\) The cross-sectional area of the tap is \(10^{-4}\,m^2.\) Assume that the pressure is constant throughout the stream of water and that flow is streamlined. The cross-sectional area of the stream, \(0.15\,m\) below the tap would be: (take \(g = 10\,ms^{-2}\) )