In the figure shown \(ABC\) is a uniform wire . If centre of mass of wire lies vertically below point \(A\) , then \(\frac{{BC}}{{AB}}\) is close to 

\(\sigma\) is the uniform surface charge density of a thin spherical shell of radius \(R\). The electric field at any point on the surface of the spherical shell is _______.

One end of a massless spring of spring constant \(k\) and natural length \(l_{0}\) is fixed while the other end is connected to a small object of mass \(m\) lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity \(\omega\) about an axis passing through fixed end, then the elongation of the spring will be

Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is \(16\). The intensity of the waves are in the ratio

The mass of the moon is \(1 / 144\) times the mass of a planet and its diameter \(1 / 16\) times the diameter of a planet. If the escape velocity on the planet is \(\mathrm{v}\), the escape velocity on the moon will be _______.

A plano-convex lens (focal length \(f_2,\) refractive index \(\mu _2,\) radius of curvature \(R\) ) fits exactly into a plano-concave lens (focal length \(f_1,\) refractive index \(\mu _1,\) radius of curvature \(R\) ). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be

The electric field in an electromagnetic wave is given by \(\overrightarrow{\mathrm{E}}=\hat{\mathrm{i}} 40 \cos \omega\left(\mathrm{t}-\frac{\mathrm{z}}{\mathrm{c}}\right) N \mathrm{NC}^{-1}\). The magnetic field induction of this wave is (in SI unit) _______.

An organ pipe \(40\,cm\) long is open at both ends. The speed of sound in air is \(360\,ms ^{-1}\). The frequency of the second harmonic is \(...........\,Hz\).

A string of length \(1\, m\) and mass \(5\, g\) is fixed at both ends. The tension in the string is \(8.0\, N\). The string is set into vibration using an external vibrator of frequency \(100\, Hz\). The separation between successive nodes on the string is close to .... \(cm\)

A body of mass \(m\) is taken from the surface of earth to a height equal to twice the radius of earth (\(R_e\)). The increase in potential energy will be _______.
(\(g\) is acceleration due to gravity at the surface of earth)

A thin bar of length \(L\) has a mass per unit length \(\lambda \), that increases linearly with distance from one end. If its total mass is \(M\) and its mass per unit length at the lighter end is \(\lambda_0\), then the distance of the centre of mass from the lighter end is