At the poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting to produce resonance with same fork, the vibrating length of wire

A steel wire of length / has a magnetic moment $M$. It is then bent into a semicircular arc. The new magnetic moment is

The angle subtended by the vector $A=4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+12 \hat{\mathbf{k}}$ with the $X$-axis is

$N$ number of balls of mass $m \mathrm{~kg}$ moving along positive direction of $X$ - axis, strike a wall per second and return elastically. The velocity of each ball is $u \mathrm{~m} / \mathrm{s}$. The force exerted on the wall by the balls in newton, is