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Grade: 10


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?

8 months ago

Answers : (2)

Vikas TU
13783 Points
Dear student
We can use cross check method.
Let m1 = 1 kg
m2 = 2 kg and
m3 = 3 kg
Suppose 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 be
a1, (a1 − a2) and (a1 + a2)
From figure 2, T − 1g − 1a1 = 0    …(i)
From figure 3,
T/2-2g-2(a1-a2)=0    …ii
From figure 4,
T/2-3g-3(a1+a2)=0    …iii
From 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:
Then  a1-a2=2g/29-19g/29
= -17g/ 29
and a1+a2=2g/29+19g/29
So, accelerations of m1, m2 and m3 are

19g/29up, 17g/29 down and 21g/29down, respectively.
Now, u = 0, s = 20 cm = 0.2 m
 ∴ s=ut+1/2at
⇒t=0.25 s
8 months ago
Sayantan Garai
117 Points
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. 
8 months ago
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