A 30 kg boy stands at the far edge of a floating plank, whose near edge is against the shore of a river. The plank is 10 m long and weighs 10 kg. If the boy walks to the neat edge of the plank, how far from the shore does the plank move

Options

A. 7m
B. 8m
C. 7.5m
D. 15m

Answer

C

Explanation

COM fo system remains at same position in absence of any external force.
Position (x - coordinate ) of COM initially (taking origin at shore is )
`x_(COM) = (m_1 x_1 + m_2 x_2)/(m_1 + m_2)`
` = (10 xx 5 + 30 xx 10)/( 10 + 30) = 35/4 m `
When boy changes his position ,let the plank moves by distance d, then
`x_(COM) = (m_1 x_1. + m_2 x_2.)/(m_1 + m_2)`
` rArr 35/4 = (10 (5 + d) + 30 d)/(10 + 30) rArr 350 =50 + 40 d `
`rArr 300/40 = d " " rArr d = 7.5 m`