A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm . If D and d are the total distance and displacement covered by the particle in 12.5 s , then \(\frac{\mathrm{D}}{\mathrm{d}}\) is ________.

Two cells of emf \(2\, E\) and \(E\) with internal resistance \(r _{1}\) and \(r _{2}\) respectively are connected in series to an external resistor \(R\) (see \(figure\)). The value of \(R ,\) at which the potential difference across the terminals of the first cell becomes zero is

Consider a circular loop that is uniformly charged and has a radius \(\mathrm{a} \sqrt{2}\). Find the position along the positive z -axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin :

Consider a mixture of \(n\) moles of helium gas and \(2 n\) moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its \(\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}\) value will be

If earth has a mass nine times and radius twice to the of a planet \(P\). Then \(\frac{v_e}{3} \sqrt{x}\; ms ^{-1}\) will be the minimum velocity required by a rocket to pull out of gravitational force of \(P\), where \(v_e\) is escape velocity on earth. The value of \(x\) is

In a Young's double slit experiment, two slits are located 1.5 mm apart. The distance of screen from slits is 2 m and the wavelength of the source is 400 nm. If the 20 maxima of the double slit pattern are contained within the centre maximum of the single slit diffraction pattern, then the width of each slit is \(\mathrm{x} \times 10^{-3} \mathrm{~cm}\), where x -value is ________.

The dimension of stopping potential \(\mathrm{V}_{0}\) in photoelectric effect in units of Planck's constant \(h\), speed of light \(c\) and Gravitational constant \(G\) and ampere \(A\) is

A particle of mass \(0.50 \mathrm{~kg}\) executes simple harmonic motion under force \(\mathrm{F}=-50\left(\mathrm{Nm}^{-1}\right) \mathrm{x}\). The time period of oscillation is \(\frac{x}{35} s\). The value of \(x\) is _______. (Given \(\pi=\frac{22}{7}\) )

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 ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures, \(\mathrm{T}_{1}\) and \(\mathrm{T}_{2} .\) The temperature of the hot reservoir of the first engine is \(\mathrm{T}_{1}\) and the temperature of the cold reservoir of the second engine is \(\mathrm{T}_{2} . T\) is temperature of the sink of first engine which is also the source for the second engine. How is \(T\) related to \(\mathrm{T}_{1}\) and \(\mathrm{T}_{2}\), if both the engines perform equal amount of work?

For a moving coil galvanometer, the deflection in the coil is \(0.05\,rad\) when a current of \(10\,mA\) is passed through it. If the torsional constant of suspension wire is \(4.0 \times 10^{-5}\,Nm\,rad ^{-1}\), the magnetic field is \(0.01\,T\) and the number of turns in the coil is \(200\),the area of each turn (in \(cm ^2\) ) is :