Question

A uniform rod of length 'l' is kept vertically on a horizontal smooth surface at a point O. If it is rotated slightly and released, it falls down on the horizontal surface. the lower end will remain

• A. at O
• B. at a distance less than l/2 from O
• C. at a distance l/2 from O
• D. at a distance larger than l/2 from O

Answer 1

The correct option is C at a distance l/2 from O

${\overrightarrow{F}}_{ext}=m{\overrightarrow{a}}_{cm}$

Along x-direction

${\overrightarrow{F}}_{ext}=0$

$\Rightarrow$ ${\overrightarrow{a}}_{c.m}=0$ (along x-direction)

$\Rightarrow$ ${\overrightarrow{V}}_{c.m}=$ Constant (along x-direction)

$\because$ Initial velocity of centre of mass is 0.

${\left({\overleftarrow{V}}_{c.m}\right)}_{final}=0$ (along x-direction)

$\Rightarrow$ x coordinate of centre of mass will remain at same point.