Question

A bar of m = 1.00 kg and length l = 0.20 m is lying on a horizontal frictionless surface. One end of the bar is pivoted so that the bar is free to rotate in the vertical plane. a small m = 0.10 kg is moving on the same horizontal surface with 5.00 ms-1 speed on its path which is perpendicular to the bar. Its hits the bar at a distance $\frac{L}{2}$ from the pivoted end and return back on the same path with speed v. After this elastic collision, the bar rotates with an angular velocity ω. Which of the following statement is correct?

• A. ω = 3.75 rad/s and v = 7.30 m/s
• B. ω = 6.80 rad/s and v = 9.10 m/s
• C. ω = 3.75 rad/s and v = 10.0 m/s
• D. ω = 6.98 rad/s and v = 4.30 m/s

Answer 1

Answer: (D)

ω = 6.98 rad/s and v = 4.30 m/s

Answer 2

For the (rod+ball) system:
(i)The angular momentum remains constant only along with hinge axis.
the hinge axis = Li=Lf
0+(0.1)(5)(0.1)=($\frac{1(0.2)^2}{3}$)\omega$$- (0.1)(v)(0.1)
= $\frac{4\omega}{3}-v=5\,\,\,.........(1)$
(ii) $e=\frac{\omega(0.1)+v}{5} where\,\, e=1$
$\frac{\omega}{10}+v=5=6.98\,\, rad/sec$
v=4.30 m/sec.