The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass \(4\;kg\). (The coordinates of the same are shown in figure) are

M and R be the mass and radius of a disc. A small disc of radius \(R / 3\) is removed from the bigger disc as shown in figure. The moment of inertia of remaining part of bigger disc about an axis AB passing through the centre O and perpendicular to the plane of disc is \(\frac{4}{x} M R^2\). The value of \(x\) is ________.

An ideal cell of emf \(10\, V\) is connected in circuit shown in figure. Each resistance is \(2\, \Omega .\) The potential difference (in \(V\)) across the capacitor when it is fully charged is

Consider two solid spheres of radii \(\mathrm{R}_{1}=1 \;\mathrm{m}\) \(\mathrm{R}_{2}=2\; \mathrm{m}\) and masses \(\mathrm{M}_{1}\) and \(\mathrm{M}_{2},\) respectively. The gravitational field due to sphere \((1)\) and \((2)\) are shown. The value of \(\frac{\mathrm{M}_{1}}{\mathrm{M}_{2}}\) is

An electric field \(\overrightarrow{\mathrm{E}}=(2 \mathrm{xi}) \mathrm{NC}^{-1}\) exists in space. \(\mathrm{A}\) cube of side \(2 \mathrm{~m}\) is placed in the space as per figure given below. The electric flux through the cube is _______ \(\mathrm{Nm}^2 / \mathrm{C}\)

In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by \(\hat{ k }\) and \(2 \hat{ i }-2 \hat{ j },\) respectively What is the unit vector along direction of propagation of the wave.

A circular disc has radius \(R_1\) and thickness \(T_1\). Another circular disc made of the same material has radius \(R_2\) and thickness \(T_2\). If the moment of inertia of both discs are same and \(\frac{R_1}{R_2}=2\) then \(\frac{T_1}{T_2}=\frac{1}{\alpha}\).The value of \(\alpha\) is __________ .

The current sensitivity of a galvanometer can be increased by: \((A)\) decreasing the number of turns \((B)\) increasing the magnetic field \((C)\) decreasing the area of the coil \((D)\) decreasing the torsional constant of the spring Choose the most appropriate answer from the options given below.

A thin infinite sheet charge and an infinite line charge of respective charge densities \(+\sigma\) and \(+\lambda\) are placed parallel at \(5\,m\) distance from each other. Points \(P\) and \(Q\), are at \(\frac{3}{\pi} m\) and \(\frac{4}{\pi} m\) perpendicular distance from line charge towards sheet charge, respectively. \(E_P\) and \(E_Q\) are the magnitudes of resultant electric field intensities at point \(P\) and \(Q\), respectively. If \(\frac{E_p}{E_Q}=\frac{4}{a}\) for \(2|\sigma|=|\lambda|\). Then the value of \(a\) is ...........

The energy of an electromagnetic wave contained in a small volume oscillates with

Given below are two statements: Statement \(I:\) Rotation of the earth shows effect on the value of acceleration due to gravity \((g)\). Statement \(II:\) The effect of rotation of the earth on the value of \(g\) at the equator is minimum and that at the pole is maximum. In the light of the above statements, choose the correct answer from the options given below.