Question

the maximum tension a rope can withstand is 60kg wt.The ratio of maximum acceleration with which two boys can climb the rope with their masses 20kg and 30kg is ....?

Answer 1

Answer:

2:1

Explanation:

The maximum tension in the rope

$T=60$ kg-wt

or, $T=60\times 10=600$ N

If the acceleration of the boys are$a_1$ and $a_2$ respectively then

$T-m_1g=m_1a_1$

$\implies 600-20\times 10=20a_1$

$\implies 600-200=20a_1$

$\implies a_1=\frac{400}{20}=20$ m/s^2

Simliarly

$T-m_2g=m_2a_2$

$\implies 600-30\times 10=30a_2$

$\implies 600-300=30a_2$

$\implies a_2=\frac{300}{30}=10$ m/s^2

Thus

$a_1:a_2=20:10=2:1$

Hope this helps.