Question

A particle of mass m moves along a curve $y = x^2$. When particle has $x -co$-ordinate as $1/2$ and $x$-component of velocity as $4m/s$. Then pick the incorrect statements:

• A. The position coordinate of particle are $(1/2, 1/4)$.
• B. The velocity of particle will be along the line $4x -4y -1 =0$.
• C. The magnitude of velocity at that instant is $4\sqrt{2}\, m/s$
• D. The magnitude of angular momentum of particle about origin at that position is 0

Answer 1

Answer: (D)

$y=x^{2}$
at $x=\frac{1}{2}, y=\frac{1}{4}$
so position is $\left(\frac{1}{2}, \frac{1}{4}\right)$
$V_{x}=4, \frac{d y}{d t}=2 x \frac{d x}{d t}$
$V _{ y }=2 xV _{ x }$
at $V_{x}=4$
$V_{y}=2\left(\frac{1}{2}\right) 4$
$V_{y}=4$
$\left(\frac{1}{2}, \frac{1}{4}\right)$