Question

The upper end of the string of a simple pendulum is fixed to a vertical z-axis, and set in motion such that the bob moves along a horizontal circular path of radius $2m$, parallel to the xy plane, $5m$ above the origin. The bob has a speed of $3m/s$. The string breaks when the bob is vertically above the x-axis, the it lands on the xy plane at a point (x, y).

• A. $x=2m$
• B. $x>2m$
• C. $y=3m$
• D. $y=5m$

Answer 1

Answer: (A), (C)

$x=2m$
$y=3m$

When the string breaks, the particle starts from the point (2, 0, 5) with speed $u_y=3m/s$, and moves as a projectile as shown in the figure.
Using $s=ut+\frac{1}{2}a{t}^2$, we get
$5=0t-\frac{1}{2}g{t}^2$.
Thus it will reach the xy plane in 1 second.
And the range i.e the y distance it will travel will be $s=ut$
or
$s=3\left(1\right)=3m$
Thus option A and C are correct.