An unpolarised light beam of intensity \(2 I _{0}\) is passed through a polaroid \(P\) and then through another polaroid \(Q\) which is oriented in such a way that its passing axis makes an angle of \(30^{\circ}\) relative to that of \(P\). The intensity of the emergent light is.

A \(2\,meter\) long scale with least count of \(0.2\,cm\) is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at \(80\,cm\) mark and \(1\,m\) mark, respectively. The image of the object pin on the other side of lens coincides with image pin that is kept at \(180\,cm\) mark. The \(\%\) error in the estimation of focal length is

A force of \(40\, N\) acts on a point \(B\) at the end of an \(L-\) shaped object, as shown in the figure. The angle \(\theta\) that will produce maximum moment of the force about point \(A\) is given by

A body of mass \(50 \mathrm{~kg}\) is lifted to a height of \(20 \mathrm{~m}\) from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases will be _______.

A sonometer wire of resonating length \(90 \mathrm{~cm}\) has a fundamental frequency of \(400 \mathrm{~Hz}\) when kept under some tension. The resonating length of the wire with fundamental frequency of \(600 \mathrm{~Hz}\) under same tension ________ \(\mathrm{cm}\).

A thermodynamic system is taken from an original state \(A\) to an intermediate state \(B\) by a linear process as shown in the figure. It's volume is then reduced to the original value from \(B\) to \(C\) by an isobaric process. The total work done by the gas from \(A\) to \(B\) and \(B\) to \(C\) would be :

An example of a perfect diamagnet is a superconductor. This implies that when a superconductor is put in a magnetic field of intensity \(B\), the magnetic field \(B_s\) inside the superconductor will be such that

The refractive index of a prism with apex angle \(A\) is \(\cot A / 2\). The angle of minimum deviation is _______.

Electrons are accelerated through a potential difference \(V\) and protons are accelerated through a potential difference \(4\, V\). The de-Broglie wavelengths are \(\lambda_e \) and \(\lambda_p \) for electrons and protons respectively. The ratio of \(\frac{{{\lambda _e}}}{{{\lambda _p}}}\) is given by : (given \(m_e\) is mass of electron and \(m_p\) is mass of proton).

Two different wires having lengths \(L _{1}\) and \(L _{2}\) and respective temperature coefficient of linear expansion \(\alpha_{1}\) and \(\alpha_{2},\) are joined end-to-end. Then the effective temperature coefficient of linear expansion is

If the velocity of a body related to displacement \({x}\) is given by \(v=\sqrt{5000+24 {x}} \;{m} / {s}\), then the acceleration of the body is \(\ldots \ldots {m} / {s}^{2}\)