163- In the figure below, $M = 2000\,\text{kg}$ and $m = 2400\,\text{kg}$. If the system is released from rest, the acceleration of mass $M$ is approximately how many $\dfrac{m}{s^2}$ and in which direction? ($g = 10\dfrac{m}{s^2}$, and the mass of the rope and pulleys are neglected.)
[Figure: A pulley system with mass $M$ hanging on one side and mass $m$ on the other side]

• [(1)] 1.5 and upward
• [(2)] 3 and upward
• [(3)] 1.5 and downward
• [(4)] 3 and downward

A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (vertically). If the acceleration of the system is $g/8$, then the ratio of the masses is
(1) $8 : 1$
(2) $9 : 7$
(3) $4 : 3$
(4) $5 : 3$

A mass $m$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $m$ and radius $R$. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass $m$, if the string does not slip on the pulley, is
(1) g
(2) $\frac{2}{3}\mathrm{~g}$
(3) $\frac{g}{3}$
(4) $\frac{3}{2}g$

Two masses $M _ { 1 }$ and $M _ { 2 }$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M _ { 2 }$ is twice that of $M _ { 1 }$, the acceleration of the system is $a _ { 1 }$. When the mass $M _ { 2 }$ is thrice that of $M _ { 1 }$, the acceleration of the system is $a _ { 2 }$. The ratio $\frac { a _ { 1 } } { a _ { 2 } }$ will be
(1) $\frac { 1 } { 3 }$
(2) $\frac { 2 } { 3 }$
(3) $\frac { 3 } { 2 }$
(4) $\frac { 1 } { 2 }$

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)

Q3. 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) $9 : 7$