Two rods \(A\) and \(B\) of identical dimensions are at temperature \(30\,^oC\). If a heated upto \(180\,^oC\) and \(B\) upto \(T\,^oC\), then the new lengths are the same. If the ratio of the coefficients of linear expansion of \(A\) and \(B\) is \(4:3\), then the value of \(T\) is........\(^oC\)

Half lives of two radioactive nuclei \(A\) and \(B\) are \(10\, minutes\) and \(20\, minutes\), respectively. If, initially a sample has equal number of nuclei, then after \(60\) \(minutes\) , the ratio of decayed numbers of nuclei \(A\) and \(B\) will be

A block of metal weighing \(2 \,kg\) is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of \(1 \,kgs ^{-1}\) and at a speed of \(10 \,ms ^{-1}\). Then, the initial acceleration of the block, in \(ms ^{-2}\), will be .................

In a photoelectric experiment ultraviolet light of wavelength \(280\, {nm}\) is used with lithium cathode having work function \(\phi=2.5\, {eV}\). If the wavelength of incident light is switched to \(400\, {nm}\), find out the change in the stopping potential (in \({V}\)). \(\left({h}=6.63 \times 10^{-34}\, {J} \cdots\right.\), \(\left.{c}=3 \times 10^{8} \,{ms}^{-1}\right)\) 

A heavy iron bar, of weight \(\mathrm{W}\) is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle \(\theta\) with the horizontal. The weight experienced by the person is _______.

A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of original objective lens. To retain same magnification keeping the object distance unchanged, the tube length has to be

Consider a tank made of glass (refractive index \(1.5\)) with a thick bottom. It is filled with a liquid of refractive index \(\mu \). A student finds that, irrespective of what the incident angle \(I\) (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of \(\mu \) is

A moving coil galvanometer has resistance \(50\,\Omega \) and it indicates full deflection at \(4\,mA\) current. A voltmeter is made using this galvanometer and a \(5\,k\Omega \) resistance. The maximum voltage, that can be measured using this voltamenter, will be close to ......\(V\)

An insulated copper wire of \(100\) turns is wrapped around a wooden cylindrical core of the crosssectional area \(24\,cm ^2\). The two ends of the wire are connected to a resistor. The total resistance in the circuit is \(12\,\Omega\). If an externally applied uniform magnetic field in the core along its axis changes from \(1.5 T\) in one direction to \(1.5\,T\) in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be \(.........\,mC\).

A stone of mass \(900 \mathrm{~g}\) is tied to a string and moved in a vertical circle of radius \(1 \mathrm{~m}\) making \(10\  \mathrm{rpm}\). The tension in the string, when the stone is at the lowest point is _______. (if \(\pi^2=9.8\) and \(g=9.8 \mathrm{~m} / \mathrm{s}^2\) )

When an object is kept at a distance of \(30\, cm\) from a concave mirror, the image is formed at a distance of \(10\, cm\) from the mirror. If the object is moved with a speed of \(9\, cms ^{-1}\), the speed (in \(cms ^{-1}\) ) with which image moves at that instant is\(....m/s\)

A wire of resistance \(R\) and radius \(r\) is stretched till its radius became \(r / 2\). If new resistance of the stretched wire is \(xR\), then value of \(x\) is _______.