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Question

The maximum tension a rope can withstand is $$60\ kgwt$$. 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:


A
1:2
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B
2:1
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C
4:3
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D
3:2
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Solution

The correct option is D $$3:2$$
Given: Maximum tension $$=60\ kgwt$$
            $$M_1=20\ kg$$ and $$M_2=30\ kg$$

$$\Rightarrow 60g=20(g+a_1)+30(g+a_2)$$
$$\Rightarrow 60g=20g+20a_1+30g+30a_2$$
$$\Rightarrow 20a_1+30a_2 =10g$$
$$\Rightarrow 2a_1+3a_2=g$$
So, the pair of values which can satisfy the above equation is:
$$a_1=\dfrac{g}{4}$$ and $$a_2=\dfrac{g}{6}$$
$$\Rightarrow a_1:a_2=3:2$$

511761_475926_ans.png

Physics

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