One end of a light inextensible string is fixed to the ceiling. The string passes under a movable pulley P, then over a fixed pulley, and its free end carries block A. If A has downward acceleration 4 m/s², acceleration of movable pulley P is:
Options

Question

One end of a light inextensible string is fixed to the ceiling. The string passes under a movable pulley P, then over a fixed pulley, and its free end carries block A. If A has downward acceleration 4 m/s², acceleration of movable pulley P is:

Options

G1 Physics · Accepted Answer

If y is downward displacement of movable pulley and x that of free end A, constant string length gives 2y + x = constant (with consistent downward coordinates). Therefore 2a_P + a_A = 0. With a_A = +4 m/s² downward, a_P = -2 m/s², i.e. 2 m/s² upward.