A wooden plank of mass M and length L is floating in still water. A persons of mass m starts at one end of the plank and reachesto other end other end in time t_(0), moving with a constant speed. Choose the correct option. (i) The speed of the person as seen from the ground is smaller than (L)/(t_(0)). (ii) The speed of the plank as seen from the ground is ((m)/(m + M)) (L)/(t_(0)). (iii) The speed of the plank as seen from the ground is ((M)/(m + M))(L)/(t_(0)). (iv) The total K.E. of the system is (1)/(2) (m + M)((L)/(t_(0)))^(2).

A wooden plank of mass M and length L is floating in still water. A pe

1.	A wooden plank of mass M and length L is floating in still water. A persons of mass m starts at one end of the plank and reachesto other end other end in time t_(0), moving with a constant speed. Choose the correct option. (i) The speed of the person as seen from the ground is smaller than (L)/(t_(0)). (ii) The speed of the plank as seen from the ground is ((m)/(m + M)) (L)/(t_(0)). (iii) The speed of the plank as seen from the ground is ((M)/(m + M))(L)/(t_(0)). (iv) The total K.E. of the system is (1)/(2) (m + M)((L)/(t_(0)))^(2).
Answer» `(i) ,(ii)` `(i),(III)` `(i) ,(iii) ,(IV)` `(i),(ii),(iv)` Solution :Velocity of the man with respect to the plank is `u = (L)/(t_(0))` When the man moves to the left , the plank moves to the right. Velocity of the plank w.r.t. the ground `= v` Velocity of the man w.r.t. the ground ` = u - v` By the momentum conservation `m(u -v) = Mv rArr v = (MU)/(M + m)` Velocity of the man w.r.t. the ground `= u -v` `(Mu)/(M + m) = ((M)/(M + m)) ((L)/(t_(0))) LT ((L)/(t_(0)))` (i) is `O.K.` `v = ((m u)/(m + M)) = ((m)/(m + M)) ((L)/(t_(0)))` (ii) is `O.K.` `K.E`. of the system `= (1)/(2) Mv^(2) + (1)/(2) m(u - v)^(2)` `= (1)/(2) ((m M)/(m + M))((L)/(t_(0)))^(2)` (iv) is wrong.