Two masses $m _ { 1 } = 5 \mathrm {~kg}$ and $m _ { 2 } = 4.8 \mathrm {~kg}$ tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when lift free to move ( $\mathrm { g } = 9.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$ )
(1) $0.2 \mathrm {~m} / \mathrm { s } ^ { 2 }$
(2) $9.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$
(3) $5 \mathrm {~m} / \mathrm { s } ^ { 2 }$
(4) $4.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$

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) $\frac { 3 \mathrm { mg } } { 4 \mathrm {~A} }$

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.

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)

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass 2 kg is:
(1) $g$
(2) $\frac { g } { 3 }$
(3) $\frac { g } { 2 }$
(4) $\frac { g } { 4 }$

A light unstretchable string passing over a smooth light pulley connects two blocks of masses $m _ { 1 }$ and $m _ { 2 }$. If the acceleration of the system is $\frac { g } { 8 }$, then the ratio of the masses $\frac { m _ { 2 } } { m _ { 1 } }$ is :
(1) $8 : 1$
(2) $5 : 3$
(3) $4 : 3$
(4) $9 : 7$

Q4. A light string passing over a smooth light pulley connects two blocks of masses $m _ { 1 }$ and $m _ { 2 }$ (where $m _ { 2 } > m _ { 1 }$ ). If the acceleration of the system is $\frac { g } { \sqrt { 2 } }$, then the ratio of the masses $\frac { m _ { 1 } } { m _ { 2 } }$ is:
(1) $\frac { 1 + \sqrt { 5 } } { \sqrt { 5 } - 1 }$
(2) $\frac { \sqrt { 2 } - 1 } { \sqrt { 2 } + 1 }$
(3) $\frac { 1 + \sqrt { 5 } } { \sqrt { 2 } - 1 }$
(4) $\frac { \sqrt { 3 } + 1 } { \sqrt { 2 } - 1 }$