Question

A uniform rod of mass m and length l is placed in gravity free space and linear impulse J is given to the rod at a distance x = l/4 from centre and perpendicular to the rod. Point A is at a distance l/3 from centre as shown in the figure. Then

• A. Speed of centre of rod is $\frac{J}{m}$
• B. Speed of point A is zero
• C. Speed of upper end of rod is $\frac{J}{2m}$
• D. Speed of lower end of rod is $\frac{5}{2}\frac{J}{m}$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A Speed of centre of rod is $\frac{J}{m}$
B Speed of point A is zero
C Speed of upper end of rod is $\frac{J}{2m}$
D Speed of lower end of rod is $\frac{5}{2}\frac{J}{m}$

$J\frac{l}{4}=\frac{m{l}^2}{12}\omega \Rightarrow \omega =\frac{3J}{ml},V_{cm}=\frac{J}{m}$

$V_A=V_{cm}-\frac{l}{3}\omega =0,V_{\text{upper}}=|V_{cm}-\frac{1}{2}\omega |=\frac{J}{2m}$

$V_{\text{lower}}=|V_{cm}+\frac{1}{2}\omega |=\frac{5}{2}\frac{J}{m}$

$\therefore$ (A)(B)(C) and (D)