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4-1.Newton's Laws of Motion
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Two balls of mass $M$ and $2 \,M$ are thrown horizontally with the same initial velocity $v_{0}$ from top of a tall tower and experience a drag force of $-k v(k > 0)$, where $v$ is the instantaneous velocity. then,
Athe heavier ball will hit the ground further away than the lighter ball
Bthe heavier ball will hit the ground closer than the lighter ball
Cboth balls will hit the ground at the same point
Dboth balls will hit the ground at the same time
(KVPY-2018)
Solution
$(a)$ Only force resisting motion of particle in horizontal direction is drag force given by
$F=-k v$
$\text { But } F=m \cdot a_{x}$
where, $a_{x}=$ acceleration in $x$-direction caused by drag force.
$\therefore \quad m a_{x}=-k v \Rightarrow a_{x}=-\frac{k v}{m}$
$\therefore$ Acceleration of particle is $x$-direction is inversely proportional to mass.
So, decreases in velocity in $x$-direction for lighter particle will be more.
Hence, heavier mass will hit the ground further away from the lighter ball.
$F=-k v$
$\text { But } F=m \cdot a_{x}$
where, $a_{x}=$ acceleration in $x$-direction caused by drag force.
$\therefore \quad m a_{x}=-k v \Rightarrow a_{x}=-\frac{k v}{m}$
$\therefore$ Acceleration of particle is $x$-direction is inversely proportional to mass.
So, decreases in velocity in $x$-direction for lighter particle will be more.
Hence, heavier mass will hit the ground further away from the lighter ball.
Standard 11
Physics
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