A car of mass `m` is initially at rest on the boat of mass `M` tied to the wall of dock through a massless, inextensible string. The car accelerates from rest to velocity `v_(0)` in times to. At `t = t_(0)` the car applies brake and comes to rest relative to the boat in negligible time. Neglect friction between the boat and water: the time `'t'` at which boat will strike the wall is

Options

A. `(L(M+m))/(mv_(0))`
B. `t_(0)+(L(M+m))/(mv_(0))`
C. `t_(0)+(L(M+m))/(Mv_(0))`
D. none of these

Answer

B

Explanation

Till time `t_(0)` frictionon car will be forward direction and on boat in backward direction. So the boat will not move till `v_(0)`. Let `v` be the velocity of car`+`boat system just after applying the brakes. From coservation of momentum.
`(m+M)v=mv_(0)impliesv=(mv_(0))/(m+M)`
Time taken `t_(0)+L/v=v_(0)(L(m+M))/(mv_(0))`