A coin placed on a rotating table just slips when it is placed at a distance of \(1\,cm\) from the center. If the angular velocity of the table in halved, it will just slip when placed at a distance of from the centre \(............\,cm\)

The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength \(6630 \; \mathring A\) is \(0.42 \; V\). If the threshold frequency is \(x \times\) \(10^{13}  / s\), where \(x\) is\(\dots\) (nearest integer). (Given, speed light \(=3 \times 10^{8} \; m / s\), Planck's constant \(=6.63 \times 10^{-34} \; Js\) )

Consider a galvanometer shunted with \(5\, \Omega\) resistance and \(2\, \%\) of current passes through it. What is the resistance of the given galvanometer? (In \(\Omega\))

The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV , respectively. If we incident a light of wavelength 550 nm on these two metal surfaces, then photo-electric effect is possible for the case of

Two liquids A and B have \(\theta_{\mathrm{A}}\) and \(\theta_{\mathrm{B}}\) as contact angles in a capillary tube. If \(K=\cos \theta_A / \cos \theta_B\). then identify the correct statement:

An electric bulb rated as \(200\, {W}\) at \(100 \,{V}\) is used in a circuit having \(200\, {V}\) supply. The resistance \('R'\) that must be put in series with the bulb so that the bulb delivers the same power is \(.....\,\Omega\)

The magnifying power of a telescope with tube \(60\; \mathrm{cm}\) is \(5 .\) What is the focal length of its eye piece?......\(cm\)

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : A electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path.
Reason (R): The magnetic field in that region is along the direction of velocity of the electron. In the light of the above statements, choose the correct answer from the options given below :

When a diode is forward biased, it has a voltage drop of \(0.5\, V.\) The safe limit of current through the diode is \(10\, mA\). If a battery of emf \(1.5\, V\) is used in the circuit, the value of minimum resistance to be connected in series with the diode so that the current does not exceed the safe limit is\(.....\Omega\)

A convex lens of refractive index 1.5 and focal length \(f=18 cm\) is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is \(\alpha \times f\). The value of \(\alpha\) is ___________.
(refractive index of water \(=4 / 3\) )