question_answer

Same force acts on two bodies of different masses 3kg and 5kg initially at rest. The ratio of time required to acquire same final velocity is:

A) 5 : 3                             

B) 25 : 9   

C) 9 : 25                           

D) 3 : 5

Correct Answer: D

Solution :

[d] \[F=3aF=5a\] \[{{a}_{1}}=\frac{F}{3}{{a}_{2}}=\frac{F}{3}\] \[{{u}_{1}}=0{{u}_{2}}=0\] \[{{v}_{1}}={{u}_{1}}={{a}_{1}}{{t}_{1}}{{v}_{2}}-{{u}_{2}}={{a}_{2}}{{t}_{2}}\] \[{{v}_{1}}=\frac{F}{3}{{t}_{1}}{{V}_{2}}=\frac{F}{5}{{t}^{2}}\] \[{{v}_{1}}={{v}_{2}}\] they acquire equal velocity \[\frac{F}{3}{{t}_{1}}=\frac{F}{3}{{t}_{2}}\] \[\frac{{{t}_{1}}}{3}=\frac{3}{5}\]