100 balls each of mass $m$ moving with speed $v$ simultaneously strike a wall normally and reflected back with same speed, in time $t s$ The total force exerted by the balls on the wall is
The drift velocity of electrons for a conductor connected in an electrical circuit is $V _{ d }$ The conductor in now replaced by another conductor with same material and same length but double the area of cross section The applied voltage remains same The new drift velocity of electrons will be
A rod with circular cross-section area $2\, cm ^2$ and length $40 cm$ is wound uniformly with $400$ turns of an insulated wire If a current of 0.4 A flows in the wire windings, the total magnetic flux produced inside windings is $4 \pi \times 10^{-6}\, Wb$ The relative permeability of the rod is(Given : Permeability of vacuum $\mu_0=4 \pi \times 10^{-7}\, NA ^{-2}$ )
For \(x \in \mathbb{R}\), two real‐valued functions \(f(x)\) and \(g(x)\) are such that