Two smooth blocks of masses $m$ and $3m$ are connected by an inextensible light string. If forces $F$ and $2F$ act on the blocks, find

$\left(\mathrm{a}\right)$ tension in the string, and

$\left(\mathrm{b}\right)$ acceleration of the blocks.

Consider the system as shown in the figure. The system is released from rest, find the tension in the cord connected between $1 \mathrm{kg}$ and $2 \mathrm{kg}$ blocks.

Find the acceleration of blocks and tension in the cord in the device shown in the figure. Assume no friction anywhere.

Two monkeys of masses $10 \mathrm{kg}$ and $8 \mathrm{kg}$ are moving along a vertical rope as shown in the figure. The former climbing up with an acceleration of $2 \mathrm{m} {\mathrm{s}}^{-2}$, while the later coming down with a uniform velocity of $2 \mathrm{m} {\mathrm{s}}^{-1}$. Find the tension in the rope at the fixed support.

A $20 \mathrm{kg}$ monkey has a firm hold on a light rope that passes over a frictionless pulley and is attached to a $20 \mathrm{kg}$ bunch of bananas (as shown in the figure). The monkey looks up, sees the bananas and starts to climb the rope to get them.

(a) As the monkey climbs, do the bananas move up, down or remain at rest?
(b) As the monkey climbs, does the distance between the monkey and the bananas decrease, increase or remain constant?
(c) The monkey releases its hold on the rope. What happens to the distance between the monkey and the bananas while it is falling?
(d) Before reaching the ground, the monkey grabs the rope to stop its fall. What do the bananas do?

What should be the minimum force $P$ to be applied to the string so that block of mass $m$ just begins to move up the frictionless plane?