Question

The maximum tension a rope can withstand is 60 kg wt. The ratio of maximum
accelerations with which two boys of masses 20 kg and 30 kg can climb up the rope
at the same time is
A) 1:2
B) 2:1
C) 4:3
D) 3:2
4) 1:2

Please say answer fast and with solution


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Answer 1

Answer:

Option (B) 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.

Answer 2

Answer:

answer is 3:2

Explanation:

60g= 20 [ g+a1]+30(g+a2)

60=20g+20a1+30g+30a2

20a1+30a2=10g

g=2a1+3a2

:: a1=g/4,a2=g/6

a1:a2= 3:2

I hope this answer will help u