Question

A uniform rope of mass $m$ hangs freely from a ceiling. A monkey of mass $M$ climbs up the rope with an acceleration $a$. The force exerted by the rope on the ceiling is

• A. $Ma+mg$
• B. $M(a+g)+mg$
• C. $M(a+g)$
• D. Dependent on the position of monkey on the rope.

Answer 1

The correct option is C $M(a+g)$

net force exerted by the rope on the ceiling = force exerted by the rope itself on the ceiling+ force exerted by the monkey on the ceiling

$T=T_1+T_2$

from diagram, we have,

$T_1=mg$

$T_2-Mg=Ma\Rightarrow T_2=M(g+a)$

$\therefore T=M(g+a)+mg$ newton's 3rd law.