The displacement equations of two waves are given as $y_1 = 10 \sin(3\pi t + \pi/3)$ and $y_2 = 5(\sin 3\pi t + \sqrt{3} \cos 3\pi t)$. What is the ratio of their amplitudes?

The cubic unit cell of a metal (molar mass $= 63.55 \ g \ mol^{-1}$) has an edge length of $362 \ pm$. Its density is $8.92 \ g \ cm^{-3}$. The type of unit cell is

$A$ circular disc is rolling on a horizontal plane. Its total kinetic energy is $300 \ J$. What is its translational kinetic energy?

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$,then the angle between them is

$A$ block of $3\,kg$ is initially in equilibrium and is hanging by two identical springs $A$ and $B$ as shown in the figure. If spring $A$ is cut from the lower point at $t=0$,then find the acceleration of the block in $m/s^2$ at $t=0$. (Take $g = 10\,m/s^2$)