A mass M=40kg is fixed at the very edge oa a long plank of mass 80kg and length 1 m which is privoted such that it is in equilibrium. How far (approx.) from the pivot should a mass of 100kg be attached so that the plank starts rotating with an angular acceleration of 1 "rad"//s^(2)`?

Options

A. `(1)/(75)m`
B. `(1)/(25)m`
C. `(1)/(15)m`
D. `(1)/(45)m`

Explanation

`80gl=40g((1)/(2)-1)`
`2l=(1)/(2)-l`
`3l=(1)/(2)`
`l=(1)/(6)m`
`100xx x=1alpha`
`=((80xxt^(2))/(12)+80xx((1)/(6))^(2)+40xx((1)/(3))^(2)+100xx x^(2))xx1`
`rArr1000x=((80)/(12)+(80)/(36)+(40)/(9)+100x^(2))`
`=((240+80+160+3600x^(2))/(36)`
`300x^(2)-3000x+40=0`
`rArr30x^(2)-300x+4=0`
`x=(300+-sqrt(90000-480))/(60)`
`=(300+0300(1-(480)/(90000)xx(1)/(2)))/(60)approx(240)/(300xx60)`