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Let m 2 =2 kg and m 3 =3 kg in figure. What should be the mass m 1 so that it remains at rest?

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8 months ago

```							Dear studentWe can use cross check method.Let m1 = 1 kgm2 = 2 kg andm3 = 3 kgSuppose the block m1 moves upward with acceleration a1 and the blocks m2 and m3 have relative acceleration a2 due to the difference of weight between them.Actual acceleration of the blocks m1, m2 and m3 will bea1, (a1 − a2) and (a1 + a2)From figure 2, T − 1g − 1a1 = 0    …(i)From figure 3,T/2-2g-2(a1-a2)=0    …iiFrom figure 4,T/2-3g-3(a1+a2)=0    …iiiFrom equations (i) and (ii), eliminating T, we get:1g + 1a2 = 4g + 4 (a1 + a2)5a2 − 4a1 = 3g    …(iv)From equations (ii) and (iii), we get:2g + 2(a1 − a2) = 3g − 3 (a1 − a2)5a1 + a2 = g    …(v)Solving equations (iv) and (v), we get:a1=2g/29a2=g-5a1a2=g-10g/29=19g/29Then  a1-a2=2g/29-19g/29= -17g/ 29and a1+a2=2g/29+19g/29=21g/29So, accelerations of m1, m2 and m3 are19g/29up, 17g/29 down and 21g/29down, respectively.Now, u = 0, s = 20 cm = 0.2 ma2=19g/29         ∴ s=ut+1/2at⇒0.2=1/2×19/29gt²⇒t=0.25 s
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8 months ago
```							I have asked the mass of m1 so that it remains in rest. It is not given m1=1kg. Also how you put s=0.2? I have not asked to copy - paste. Please answer the right question.
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8 months ago
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