question_answer

A 20 kg block B is suspended from a cord attached to a 40 kg cart A. Find the ratio of the acceleration of block in cases (i) and (ii) shown in the figure immediately after the system is released from rest. (neglect friction)

A) \[\frac{\sqrt{2}}{3}\]  

B) \[3\sqrt{2}\]

C)  \[\frac{3}{2}\]  

D) \[\frac{3}{2\sqrt{2}}\]

Correct Answer: D

Solution :

[d] Case I: \[T-N=40a\] \[\text{and 20g}-T=20a\] \[Also\text{   N=20a}\] \[\text{After simplifying, we get }\] \[\text{a=}\frac{g}{4}\] \[\text{Accerelation of block B, =}\sqrt{2}a=\frac{g}{2\sqrt{2}}.\] Case II: \[T=40a\] \[\text{and 20g}-\text{T=20a}\] \[\text{After simplifying above equatin, wer get }\] \[\text{a=g/3}\] \[\text{Ratio=}\frac{g/2\sqrt{2}}{g/3}=\frac{3}{2\sqrt{2}}.\]