A cube has side length 5 cm and modulus of rigidity $10^5 \mathrm{~N} / \mathrm{m}^2$. The displacement produced by a force of 10 N in the upper face of cube is $\_\_\_\_$ mm.

From 18 m height above the ground a ball is dropped from rest . The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is $\_\_\_\_$ m.

(Take $g=10 \mathrm{~m} / \mathrm{s}^2$ and neglect the air resistance)

A transverse wave on a string is described by $y=3 \sin (36 t+0.018 x+\pi / 4)$. where $x, y$ are in cm and $t$ in seconds. The least distance between the two successive crests in the wave is $\_\_\_\_$ cm . (Nearest integer)

$$ (\pi=3.14) $$

The charged particle moving in a uniform magnetic field of $(3 \hat{i}+2 \hat{j}) \mathrm{T}$ has an acceleration $\left(4 \hat{i}-\frac{x}{2} \hat{j}\right) \mathrm{m} / \mathrm{s}^2$. The value of $x$ is