A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (vertically). If the acceleration of the system is g/8 , then the ratio of masses is

Question

A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (vertically). If the acceleration of the system is g/8 , then the ratio of masses is (A) 8:1 (B) 9:7 (C) 4:3 (D) 5:3

Tardigrade Admin · Accepted Answer

In the given system, a=(m1 - m2/m1 + m2)=(g/8) ∴ (m1 - m2/m1 + m2)=(1/8) 8m1-8m2=m1+m2 7m1=9m2 (m1/m2)=(9/7)

Q. 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 masses is

$8 : 1$

$9 : 7$

$4 : 3$

$5 : 3$

In the given system,
$a = \frac{m _{1} - m _{2}}{m _{1} + m _{2}} = \frac{g}{8}$
$∴ \frac{m _{1} - m _{2}}{m _{1} + m _{2}} = \frac{1}{8}$
$8 m_{1} - 8 m_{2} = m_{1} + m_{2}$
$7 m_{1} = 9 m_{2}$
$\frac{m _{1}}{m _{2}} = \frac{9}{7}$

Q. A light string passing over a smooth light pulley connects two blocks of masses m1​ and m2​ (vertically). If the acceleration of the system is g/8 , then the ratio of masses is

8:1

9:7

4:3

5:3