A particle of mass \(2\, kg\) is moving such that at time \(t\), its position, in meter, is given by \(\overrightarrow r \left( t \right) = 5\hat i - 2{t^2}\hat j\) . The angular momentum of the particle at \(t\, = 2\, s\) about the origin in \(kg\, m^{-2}\, s^{-1}\) is

In a meter bridge experiment, the circuit diagram and the corresponding observation table are shown in figure

\(Sl\). \(No\).	\(R\, (\Omega )\)	\(l\, (cm)\)
\(1\).	\(1000\)	\(60\)
\(2\).	\(100\)	\(13\)
\(3\).	\(10\)	\(1.5\)
\(4\).	\(1\)	\(1.0\)

Which of the readings is inconsistent ?

The ratio of escape velocity of a planet to the escape velocity of earth will be:Given : Mass of the planet is \(16\) times mass of earth and radius of the planet is \(4\) times the radius of earth.

A flask contains Hydrogen and Argon in the ratio \(2: 1\) by mass. The temperature of the mixture is \(30^{\circ} C\). The ratio of average kinetic energy per molecule of the two gases ( \(K\) argon/ \(K\) hydrogen) is: (Given: Atomic Weight of \(Ar = 39.9\))

A fringe width of \(\,6 mm\) was produced for two slits separated by \(1\, mm\) apart. The screen is placed \(10\, m\) away. The wavelength of light used is \('x'\, nm.\) The value of \('x'\) to the nearest integer is

Width of one of the two slits in a Young's double slit interference experiment is half of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is _______.

A flask contains hydrogen and oxygen in the ratio of \(2: 1\) by mass at temperature \(27^{\circ} C\). The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is :

For a transverse wave travelling along a straight line, the distance between two peaks (crests) is \(5 \,m ,\) while the distance between one crest and one trough is \(1.5 \,m\) The possible wavelengths (in \(m\) ) of the waves are

Consider following statements for refraction of light through prism, when angle of deviation is minimum.
(A) The refracted ray inside prism becomes parallel to the base.
(B) Larger angle prisms provide smaller angle of minimum deviation.
(C) Angle of incidence and angle of emergence becomes equal.
(D) There are always two sets of angle of incidence for which deviation will be same except at minimum deviation setting.
(E) Angle of refraction becomes double of prism angle.
Choose the correct answer from the options given below.

A block of mass \(m =1\, kg\) slides with velocity \(v=6\, m / s\) on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about \(O\) and swings as a result of the collision making angle \(\theta\) before momentarily coming to rest. If the rod has mass \(M =2 \,kg \) and length \(l=1\, m\) the value of \(\theta\) is approximately (Take \(\left.g=10 \,m / s ^{2}\right)\)

A liquid drop having \(6\) excess electrons is kept stationary under a uniform electric field of \(25.5\, k\,Vm^{-1}\) . The density of liquid is \(1.26\times10^3\, kg\, m^{-3}\) . The radius of the drop is (neglect buoyancy)

Three solid spheres each of mass \(\mathrm{m}\) and diameter \(d\) are stuck together such that the lines connecting the centres form an equilateral triangle of side of length \(d\). The ratio \(\mathrm{I}_{0} / \mathrm{I}_{\mathrm{A}}\) of moment of inertia \(\mathrm{I}_{0}\) of the system about an axis passing the centroid and about center of any of the spheres \(\mathrm{I}_{\mathrm{A}}\) and perpendicular to the plane of the triangle is

The two wires \(A\) and \(B\) of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire \(A\) and wire \(B\) is \(20/11\). When the joined wire is kept under certain tension the elongations in the wires \(A\) and \(B\) are equal. If the length of wire \(A\) is \(2.2\) m, then the length of wire \(B\) is _______ m.