In the figure, the pulley P moves to the right with a constant speed u. The downward spee of A is ` v_(A)` and the speed of B to the right is ` v_(B)` . Then,

Options

A. `v_(A)= v_(B)`
B. `v_(B)= u+v_(A)`
C. `v_(B) + u =v_(A)`
D. the two blocks have accelerations of the same magnitude.

Answer

B, D

Explanation

At any instant of time, let the length of the string `BP=l_(1)` and the length ` PA= l_(2)` . In a further time t, let B move to the right by x and A move down by y, while P moves to the right by ut. As the length of the string must remain constant ,
` l_(1) + l_(2) = ( l_(1) -x + ut) + (l_(2) +y ) `
` or x = ut + y or (dx)/(dt) = u + (dy)/(dt) `
` (dx)/(dt) ` = speed of B to the right ` = v_(B)`
` (dy)/(dt) ` = downward speed of A ` = v_(A) therefore v_(B) = u+ V_(A)`
Also `d_(v_(B))/(dt) = (dv_(A))/(dt) = or a_(B) = a_(A)`