An electric dipole of mass m, charge q, and length \(l\) is placed in a uniform electric field \(\overrightarrow{\mathrm{E}}=\mathrm{E}_0 \hat{i}\). When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:

To get output ‘\(1\)’ at \(R\), for the given logic gate circuit the input values must be

The ratio of the density of oxygen nucleus \(\left({ }_8^{16} O \right)\) and helium nucleus \(\left({ }_2^4 He \right)\) is

A thin convex lens of focal length \('f'\) is put on a plane mirror as shown in the figure. When an object is kept at a distance \('a'\) from the lens - mirror combination, its image is formed at a distance \(\frac{a}{3}\) in front of the combination. The value of \('a'\) is

Two masses m and 2m are connected by a light string going over a pulley (disc) of mass 30m with radius r = 0.1 m. The pulley is mounted in a vertical plane and it is free to rotate about its axis. The 2m mass is released from rest and its speed when it has descended through a height of 3.6 m is __________ m/s. (Assume string does not slip and \( g=10 m/s^{2} \))

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 \(g=9.8 \mathrm{~m} / \mathrm{s}^2\) )

Identify the correct truth table of the given logical circuit.

A shunt of resistance \(1\,\Omega \) is connected across a galvanometer of \(120\,\Omega \) resistance. A current of \(5.5\, ampere\) gives full scale deflection in the galvanometer. The current that will give full scale deflection in the absence of the shunt is nearly ............... \(ampere\)

One mole of an ideal monoatomic gas is taken along the path \(ABCA\)  as shown in the \(PV\) diagram. The maximum temperature attained by the gas along the path \(BC\)  is given by

Three students \(S_{1}, S_{2}\) and \(S_{3}\) perform an experiment for determining the acceleration due to gravity \((g)\) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.

Student No.	Length of pendulum \((cm)\)	No. of osci \((n)\)	Total time for osci	Time period \((s)\)
\(1.\)	\(64.0\)	\(8\)	\(128.0\)	\(16.0\)
\(2.\)	\(64.0\)	\(4\)	\(64.0\)	\(16.0\)
\(3.\)	\(20.0\)	\(4\)	\(36.0\)	\(9.0\)

(Least count of length \(=0.1 \,{m}\), least count for time \(=0.1\, {s}\) ) If \(E_{1}, E_{2}\) and \(E_{3}\) are the percentage errors in \('g'\) for students \(1,2\) and \(3\) respectively, then the minimum percentage error is obtained by student no. ....... .

The work function of a metal is 3 eV. The color of the visible light that is required to cause emission of photoelectrons is _______.