The de Broglie wavelengths of a proton and an \(\alpha\) particle are \(\lambda\) and \(2 \lambda\) respectively. The ratio of the velocities of proton and \(\alpha\) particle will be _______.

The charge accumulated on the capacitor connected in the following circuit is________ \(\mu \mathrm{C}\) (Given \(\mathrm{C}=150\  \mu \mathrm{F}\))

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as \(4.62 \mathrm{~s}, 4.632 \mathrm{~s}, 4.6 \mathrm{~s}\) and \(4.64 \mathrm{~s}\). The arithmetic mean of these reading in correct significant figure is _______.

A thin disc of radius \(b = 2a\)  has a concentric hole of radius \('a'\) in it (see figure). It carries uniform surface charge \('\sigma '\) on it. If the electric field on its axis at height \('h'\) \((h << a)\) from its centre is given as \('Ch'\) then value of \('C'\) is

An infinite plane sheet of charge having uniform surface charge density \(+\sigma_5 \mathrm{C} / \mathrm{m}^2\) is placed on \(\mathrm{x}-\mathrm{y}\) plane. Another infinitely long line charge having uniform linear charge density \(+\lambda_e \mathrm{C} / \mathrm{m}\) is placed at \(z=4 \mathrm{~m}\) plane and parallel to \(y\)-axis. If the magnitude values \(\left|\sigma_s\right|=2\left|\lambda_{\mathrm{e}}\right|\) then at point \((0,0,2)\), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is \(\pi \sqrt{\mathrm{n}}: 1\). The value of \(n\) is _______.

Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is \(T\), density of liquid is \(\rho\) and \(L\) is its latent heat of vaporization

\(L\), \(C\) and \(R\) represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula \(ML^2 T^{-4} A^{-2}\) corresponds to __________.

A particle \((\mathrm{m}=1\; \mathrm{kg})\) slides down a frictionless track \((AOC)\) starting from rest at a point \(A\) (height \(2\; \mathrm{m}\) ). After reaching \(\mathrm{C}\), the particle continues to move freely in air as a projectile. When it reaching its highest point \(P\) (height \(1 \;\mathrm{m}\) ). the kinetic energy of the particle (in \(\mathrm{J}\) ) is : (Figure drawn is schematic and not to scale; take \(\left.g=10 \;\mathrm{ms}^{-2}\right)\)

Given below are two statement : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : When a rod lying freely is heated, no thermal stress is developed in it. Reason \(R :\) On heating the length of the rod increases. In the light of the above statements, choose the correct answer from the options given below

In the given figure an ammeter \(A\) consists of a \(240 \Omega\) coil connected in parallel to a \(10 \Omega\) shunt. The reading of the ammeter is _______ \(\mathrm{mA}\).

Two thin convex lenses of focal length 30 cm and 10 cm are placed coaxially, 10 cm apart. The power of this combination is :