A particle moves in the $xy-$plane under the action of a force $F$ such that the components of its linear momentum $p$ at any time $t$ are ${p_x} = 2\cos t$, ${p_y} = 2\sin t$. The angle between $F$ and $p$ at time $t$ is ........... $^o$
A particle moves in the $xy-$plane under the action of a force $F$ such that the components of its linear momentum $p$ at any time $t$ are ${p_x} = 2\cos t$, ${p_y} = 2\sin t$. The angle between $F$ and $p$ at time $t$ is ........... $^o$
$90$
$0$
$180$
$30$
A particle moves in the $xy-$plane under the action of a force $F$ such that the components of its linear momentum $p$ at any time $t$ are ${p_x} = 2\cos t$, ${p_y} = 2\sin t$. The angle between $F$ and $p$ at time $t$ is ........... $^o$
Given that $\vec p = {p_x}\hat i + {p_y}\hat j = 2\cos t\;\hat i + 2\sin t\;\hat j$
$\vec F = \frac{{d\vec p}}{{dt}} = - 2\sin t\;\hat i + 2\cos t\;\hat j$
Now, $\vec F.\vec p = 0$
i.e. angle between $\vec F\;{\rm{and }}\,\vec p$ is $90^o.$
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