A-uniform-rod-of-AB-of-mass-m-1-12-kg-and-lengtj-l-100cm-is-placed-on-a-sharp-support-O-such-that-AO-a-40cm-To-keep-the-rod-horizontal-its-end-A-is-ties-with-a-thread-Calculate-reaction-of-support-

Question Number 24460 by sushmitak last updated on 18/Nov/17

A uniform rod of AB of mass

m = 1.12 kg and lengtj l = 100 cm is

placed on a sharp support O such that

AO = a = 40 c m . To keep the rod

horizontal, its end A is ties with a

thread . Calculate reaction of support

O on the rod when the thread is burnt .

(g = 10 m \cdot s^{- 2})

Commented by sushmitak last updated on 18/Nov/17

Commented by ajfour last updated on 18/Nov/17

T o r q u e a b o u t O :

m g (\frac{b - a}{2}) = [\frac{{m l}^{2}}{12} + m {(\frac{b - a}{2})}^{2}] α

\Rightarrow α = \frac{6 g (b - a)}{l^{2} + 3 {(b - a)}^{2}}

A l s o m g - N_{O} = m α (\frac{b - a}{2})

\Rightarrow N_{O} = m g - \frac{3 m g {(b - a)}^{2}}{l^{2} + 3 {(b - a)}^{2}}

N_{O} = \frac{m g}{1 + 3 {(\frac{b - a}{l})}^{2}} .

= \frac{11.2}{1 + 0.12} = 10 N .

Commented by sushmitak last updated on 18/Nov/17

Thank You very much Sir!