If the unit of length and force be increased four times,then the unit of energy is

$A$ long straight wire along the $z$-axis carries a current $I$ in the negative $z$-direction. The magnetic vector field $\vec B$ at a point having coordinates $(x, y)$ in the $z = 0$ plane is

The masses and radii of the earth and the moon are $M_1, R_1$ and $M_2, R_2$ respectively. Their centres are at a distance $d$ apart. The minimum speed with which a particle of mass $m$ should be projected from a point midway between the two centres so as to escape to infinity is:

Among $K$,$Mg$,$Au$,and $Cu$,the one which is extracted by heating its ore in air is

If the pair of lines $ax^2 + 2(a + b)xy + by^2 = 0$ represent the diameters of a circle and divide the circle into four sectors such that the area of one sector is three times the area of the other,then:

Consider a metal sphere of radius $R$ that is cut in two parts along a plane whose minimum distance from the sphere's centre is $h$. The sphere is uniformly charged by a total electric charge $Q$. The minimum force necessary to hold the two parts of the sphere together is: