Centre of Mass 2 Question 2
3. A ball is thrown vertically up (taken as $+Z$-axis) from the ground. The correct momentum-height $(p-h)$ diagram is
(2019 Main, 9 April I) (a)
(c)
(b)
(d)
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Answer:
Correct Answer: 3. (d)
Solution:
- When a ball is thrown vertically upward, then the acceleration of the ball,
$a$ =acceleration due to gravity ( $g$ ) (acting in the downward direction).
Now, using the equation of motion,
$$ \begin{aligned} v^{2} & =u^{2}-2 g h \\ \text { or } \quad h & =\frac{-v^{2}+u^{2}}{2 g} \end{aligned} $$
As we know, momentum, $p=m v$ or $v=p / m$
So, substituting the value of $v$ in Eq. (i), we get
$$ h=\frac{u^{2}-(p / m)^{2}}{2 g} $$
As we know that, at the maximum height, velocity of the ball thrown would be zero.
So, for the flight when the ball is thrown till is reaches the maximum height $(h)$.
$v \rightarrow$ changes from $u$ to 0
$\Rightarrow p \rightarrow$ changes from $m u$ to 0
Similarly, when it reacher it’s initial point, then
$h \rightarrow$ changes from $h _{\text {max }}$ to 0
Also, $p \rightarrow$ changes from 0 to some values.
Thus, these conditions are only satisfied in the plot given in option (d).
