A ring is hung on a nail. It can oscillate, without slipping or sliding \((i)\) in its plane with a time period \(T_{1}\) and, \((ii)\) back and forth in a direction perpendicular to its plane, with a period \(T _{2}\). the ratio \(\frac{ T _{1}}{ T _{2}}\) will be 

List\(-I\)	List\(-II\)
\(UV\) rays	\((i)\) Diagnostic tool in medicine
\(X-\) rays	\((ii)\) Water purification
Microwave	\((iii)\) Communication, Radar
Infrared wave	\((iv)\) Improving visibility in foggy days

Choose the correct answer from the options given below.

A rigid square loop of side \(a\) and carrying current \(I_2\) is laying on a horizontal surface near a long current \(I_1\) wire in the same plane as shown in figure. The net force on the loop due to the wire will be

A wire of cross sectional area \(A\), modulus of elasticity \(2 \times 10^{11} \mathrm{Nm}^{-2}\) and length \(2 \mathrm{~m}\) is stretched between two vertical rigid supports. When a mass of \(2 \mathrm{~kg}\) is suspended at the middle it sags lower from its original position making angle \(\theta=\frac{1}{100}\) radian on the points of support. The value of \(A\) is _______ \(\times 10^{-4} \mathrm{~m}^2\) (consider \(\mathrm{x}<\mathrm{L}\) ). (given: \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )

Given below are two statements : Statement \(I:\) If the Brewster's angle for the light propagating from air to glass is \(\theta_{ B }\), then Brewster's angle for the light propagating from glass to air is \(\frac{\pi}{2}-\theta_B\). Statement \(II:\) The Brewster's angle for the light propagating from glass to air is \(\tan ^{-1}\left(\mu_{ g }\right)\) where \(\mu_{ g }\) is the refractive index of glass. In the light of the above statements, choose the correct answer from the options given below :

Two cells are connected between points \(A\) and \(B\) as shown. Cell \(1\) has emf of \(12\,V\) and internal resistance of \(3\,\Omega\). Cell \(2\) has emf of \(6\,V\) and internal resistance of \(6\,\Omega\). An external resistor \(R\) of \(4\,\Omega\) is connected across \(A\) and \(B\). The current flowing through \(R\) will be \(.............A\).

In an experiment a convex lens of focal length \(15\, cm\) is placed coaxially on an optical bench in front of a convex mirror at a distance of \(5\,cm\) from it. It is found that an object and its image coincide, if the object is placed at a distance of \(20\,cm\) from the lens. The focal length of the convex mirror is.......\(cm\)

A particle starts with an initial velocity of \(10.0\,ms ^{-1}\) along \(x\)-direction and accelerates uniformly at the rate of \(2.0\,ms ^{-2}\). The time taken by the particle to reach the velocity of \(60.0\,ms ^{-1}\) is \(.......\,s\)

Unpolarized light of intensity \(I\) passes through an ideal polarizer \(A\) Another indentical polarizer \(B\) is placed behind \(A\) The intensity of light beyond \(B\) is found to be \(\frac{I}{2}\) Now another identical polarizer \(C\) is placed between \(A\) and \(B\). The intensity beyond \(B\) is now found to be \(\frac{I}{8}\) The angle between polarizer \(A\) and \(C\) is:......\(^o\)

Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is \(\sqrt{2}\) times the speed of sound, then the value of \(n\) will be

A beam of unpolarised light of intensity \(I_0\) is passed through a polaroid \(A\) and then through another polaroid \(B\) which is oriented so that its principal plane makes an angle of \(45^o \) relative to that of \(A\). The intensity of the emergent light is _______.