The maximum tension a rope can withstand is 6 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the maximum accelerations of the two boys be $a_1$ and $a_2$ respectively.The total tension $T$ in the rope must not exceed $60 \,kg$-wt.The e

Vedclass · Accepted Answer

$2$ : $1$

Vedclass · Answer

(B) Let the maximum accelerations of the two boys be $a_1$ and $a_2$ respectively.The total tension $T$ in the rope must not exceed $60 \,kg$-wt.The equation of motion for the two boys climbing up is:$T = m_1(g + a_1) + m_2(g + a_2)$Given $T = 60 \,kg$-wt,$m_1 = 20 \,kg$,and $m_2 = 30 \,kg$:$60g = 20(g + a_1) + 30(g + a_2)$$60g = 20g + 20a_1 + 30g + 30a_2$$60g = 50g + 20a_1 + 30a_2$$10g = 20a_1 + 30a_2$Dividing by $10$:$g = 2a_1 + 3a_2$To find the ratio of maximum accelerations,we consider the individual limits for each boy. If only one boy were climbing,the maximum acceleration would be $a = (T/m) - g$. For boy $1$: $a_{1,max} = (60/20)g - g = 2g$. For boy $2$: $a_{2,max} = (60/30)g - g = g$.However,the question asks for the ratio of accelerations when they climb together. Assuming they climb with the same acceleration $a$ to find the limit,$g = 2a + 3a = 5a \Rightarrow a = g/5$. If we look for the ratio of their individual maximum possible accelerations,it is $2g : g = 2 : 1$. Given the options,the intended ratio is $a_1 : a_2 = 2 : 1$.

The maximum tension a rope can withstand is $60 \,kg$-wt. The ratio of maximum acceleration with which two boys of masses $20 \,kg$ and $30 \,kg$ can climb up the rope at the same time is

Similar Questions

$A$ block of mass $4 \,kg$ is suspended through two light spring balances $A$ and $B$ as shown in the figure. Then $A$ and $B$ will read respectively:

The minimum acceleration with which a fireman can slide down a rope of breaking strength two-third of his weight is

With what acceleration can a block be moved upwards using a rope,if the breaking strength of the rope is $5$ times the weight of the block?

For the given figure,find the value of $m$ (in $kg$) for which the blocks have an acceleration of $\frac{8}{13}g$. The block on the incline has a mass of $100 \, g = 0.1 \, kg$ and the hanging block on the left has a mass of $50 \, g = 0.05 \, kg$. The surface is frictionless $(\mu = 0)$.

$A$ monkey of mass $m$ is climbing a rope hanging from the roof with acceleration $a$. The coefficient of static friction between the body of the monkey and the rope is $\mu$. Find the direction and value of the friction force on the monkey.

Vedclass Test Series

Exam Paper Generator

Online Exam Module