Question

A $10\text{kg}$ monkey is climbing a massless rope attached to a $15\text{kg}$ mass over a smooth tree limb. The mass is lying on the ground. In order to raise the mass from the ground he must climb with:

• A. Acceleration greater than $5{\text{m/sec}}^2$
• B. Acceleration greater than $2.5{\text{m/sec}}^2$
• C. High speed
• D. Acceleration greater than $10{\text{m/sec}}^2$

Answer 1

The correct option is A Acceleration greater than $5{\text{m/sec}}^2$

For 15 kg to lift off the ground


For monkey FBD,


As monkey is going up with acceleration $\text{a}$ tension in the string can be given as
$T=10(\text{g}+\text{a})$
On the other side as the $15\text{kg}$ mass is at rest so, $T=15g$
Equating both the equation
$T\Rightarrow 10\text{a}+10\text{g}>15\text{g}$
$\Rightarrow \text{a}>0.5\text{g}\Rightarrow \text{a}>5{\text{m/s}}^2$