$y_{1}=5 \sin 2 \pi(x-v t) \,c m\,$
$y_{2}=3 \sin 2 \pi(x-v t+1.5) \,c m$
These waves are simultaneously passing through a string. The amplitude of the resulting wave is.........$cm$
$\Delta \theta=2 \pi(1.5)=3 \pi$
$A_{\text {net }}=\sqrt{A_{1}^{2}+A_{2}^{2}+2 A_{1} A_{2} \cos (3 \pi)}$
$=\left| A _{1}- A _{2}\right|$
$=2 \,cm$
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$[A]$ The $x$ component of displacement of the center of mass of the block $M$ is : $-\frac{m R}{M+m}$.
[$B$] The position of the point mass is : $x=-\sqrt{2} \frac{\mathrm{mR}}{\mathrm{M}+\mathrm{m}}$.
[$C$] The velocity of the point mass $m$ is : $v=\sqrt{\frac{2 g R}{1+\frac{m}{M}}}$.
[$D$] The velocity of the block $M$ is: $V=-\frac{m}{M} \sqrt{2 g R}$.
