Two bodies of masses 15gm and 25gm are connected by means of a string of length 40cm and mass 10gm. The string is made to pass over a smooth massless pulley. Initially the two bodies are kept at the same level and released. By the time the heavier mass descends by 10cm, the acceleration of the system,

Given ${\text{m}}_{\text{string}}=10\text{gm}$

$l_{\text{string}}=40\text{cm}$

Initially when two are at same level for 20 cm length mass is 5 gm

Case 1 : acceleration, $\text{a}=\left[\frac{30-20}{30+20}\right]\text{g}$

$\text{a}=\frac{10}{50}\text{g}$

$\text{a}=\frac{\text{g}}{\text{5}}=\frac{\text{2g}}{\text{10}}{\text{ms}}^{-2}$

Case 2 : when larger mass descends by 10 cm

${\text{a}}^{\text{1}}=\left[\frac{32.5-17.5}{50}\right]\text{g}$

[for 10 cm mass = 2]

${\text{a}}^1=\text{3g/10}$

$\therefore$ Acceleration increases by a factor$\frac{{\text{a}}^{\text{1}}}{\text{a}}=\frac{3}{2}=1.5$