Question

A rope of negligible mass passes over a pulley of negligible mass attached to the ceiling, as shown in figure. One end of the rope is held by Student $A$ of mass $70kg$, who is at rest on the floor. The opposite end of the rope is held by Student $B$ of mass $60kg$, who is suspended at rest above the floor. The minimum acceleration $a_0$ with which the Student $B$ should climb up the rope to lift the Student $A$ upward off the floor.

• A. $\frac{1}{3}m/s^2$
• B. $\frac{2}{3}m/s^2$
• C. $\frac{4}{3}m/s^2$
• D. $\frac{5}{3}m/s^2$

Answer 1

Answer: (D)

For student $A$ to just lift off the floor, tension $T$ in string must be greater than or equal to $700N$.
The F.B.D. of student $B$ is
Applying Newton's second law
$T-mg=ma$
$\Rightarrow 700-600=6a$
or $a=\frac{5}{3}m/s^2$