The current passing through a conducting loop in the form of equilateral triangle of side \(4\sqrt{3}\) cm is 2A. The magnetic field at its centroid is \(\alpha\times10^{-5}T\). The value of \(\alpha\) is ___________.
(Given : \(\mu_{o}=4\pi\times10^{-7}\) SI units)

If Surface tension \((S)\), Moment of Inertia \((I)\) and Planck’s constant \((h)\), were to be taken as the fundamental units, the dimensional formula for linear momentum would be

Four particles \(A, B, C\) and \(D\) with masses \(m_A=m, m_B=2m, m_C=3m\) and \(m_D=4m\) are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is

A hydraulic press can lift \(100\, kg\) when a mass \('m'\) is placed on the smaller piston. It can lift ......... \(kg\) when the diameter of the larger piston is increased by \(4\) times and that of the smaller piston is decreased by \(4\) times keeping the same mass \('m'\) on the smaller piston.

Given below are two statements: Statement \(I :\) In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution. Statement \(II :\) In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule. In the light of the above statements, choose the correct answer from the options given below:

A satellite is in an elliptical orbit around a planet \(P.\) It is observed that the velocity of the satellite when it is farthest from the planet is \(6\) time less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is\(......\)

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity \(3\, m / s\) (as shown in figure). Maximum height with respect to the initial position covered by it will be \(...........cm\).

A balloon and its content having mass \(M\) is moving up with an acceleration ' \(a\) '. The mass that must be released from the content so that the balloon starts moving up with an acceleration ' \(3 a^{\prime}\) will be
(Take ' g ' as acceleration due to gravity)

Match the LIST-I with LIST-II

LIST-I		LIST-II
A.	Pressure varies inversely with volume of an ideal gas	I.	Adiabatic process
B.	Heat absorbed goes partly to increase internal energy and partly to do work	II.	Isochoric process
C.	Heat is neither absorbed nor released by a system	III.	Isothermal process
D.	No work is done on or by a gas	IV.	Isobaric process

Choose the correct answer from the options given below:

A plane electromagnetic wave in a non-magnetic dielectric medium is given by \(\vec E\, = \,{\vec E_0}\,(4 \times {10^{ - 7}}\,x - 50t)\) with distance being in meter and time in seconds. The dielectric constant of the medium is