Atwood machine and pulley systems

Masses are connected via strings over pulleys (including Atwood machines), and the question asks for acceleration, tension, or applied force in the pulley-string system.

jee-main 2013 Q5 View
Two blocks of masses m and M are connected by means of a metal wire of cross-sectional area A passing over a frictionless fixed pulley as shown in the figure. The system is then released. If $\mathrm { M } = 2 \mathrm {~m}$, then the stress produced in the wire is:
(1) $\frac { 2 \mathrm { mg } } { 3 \mathrm {~A} }$
(2) $\frac { 4 \mathrm { mg } } { 3 \mathrm {~A} }$
(3) $\frac { \mathrm { mg } } { \mathrm { A } }$
(4) $\frac { 3 \mathrm { mg } } { 4 \mathrm {~A} }$
jee-main 2022 Q22 View
A system of 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the $7 ^ { \text {th} }$ and $8 ^ { \text {th} }$ ball is $\_\_\_\_$ N when $6 ^ { \text {th} }$ ball just leaves the table.
jee-main 2022 Q21 View
A hanging mass $M$ is connected to a four times bigger mass by using a string pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by $2Mg$ force. In this situation, tension in the string is $\frac{x}{5}Mg$ for $x =$ $\_\_\_\_$. Neglect mass of the string and friction of the block (bigger mass) with ice slab. (Given $g =$ acceleration due to gravity)