A sphere P of mass m and moving with velocity | vedclass

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Question

According to law of conservation of linear momentum, we get

$m \vec{v}_{i}+m 	imes 0=m \vec{v}_{P f}=m \vec{v}_{Q f}$

where $\vec{v}_{P f}$ and

Vedclass · Accepted Answer

$90$

Vedclass · Answer

According to law of conservation of linear momentum, we get

$m \vec{v}_{i}+m 	imes 0=m \vec{v}_{P f}=m \vec{v}_{Q f}$

where $\vec{v}_{P f}$ and $\vec{v}_{Q f}$ are the final velocities of spheres $P$ and $Q$ after collision respectively. $\vec{v}_{i}=\vec{v}_{P f}+v e v_{Q f}$

$\left(\vec{v}_{i} \cdot \vec{v}_{i}ight)=\left(\vec{v}_{P f}+\vec{v}_{Q f}ight) \cdot\left(\vec{v}_{P f}+\vec{v}_{Q f}ight)$

$\vec{v}_{P f} \cdot \vec{v}_{P f}+\vec{v}_{Q f} \cdot \vec{v}_{Q f}+2 \vec{v}_{P f} \cdot \vec{v}_{Q f}$

or $v_{i}^{2}=v_{P f}^{2}+v_{Q f}^{2}+2 v_{P f} v_{Q f} \cos 	heta \ldots$

According to conservation of kinetic energy, we get

$\frac{1}{2} m v_{i}^{2}=\frac{1}{2} m v_{P f}^{2}+\frac{1}{2} m v_{Q f}^{2} \Rightarrow v_{i}^{2}=v_{P f}^{2}+v_{Q f}^{2}$

Comparing $( i )$ and $( ii)$ we get

$2 v_{P f} v_{q f} \cos 	heta=0 \Rightarrow \cos 	heta=0$ or $	heta=90^{\circ}$

A sphere $P$ of mass $m$ and moving with velocity $v$ undergoes an oblique and perfectly elastic collision with an identical sphere $Q$ initially at rest. The angle $\theta $ between the velocities of the spheres after the collision shall be ............... $^o$

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