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Masses M(1),M(2) and M(3) are connected ...

Masses `M_(1),M_(2) and M_(3)` are connected by string of negligible mass which pass over massless and frictionless pulleys `P_(1) and P_(2)` as shown in figure 7.15. The masses move such that the string between `P_(1) and P_(2)` is parallel to the incline and the portion of the string between `P_(2) and M_(3)` is horizontal. The masses `M_(2) and M_(3)` are 4.0 kg each and the coefficient of kinetic friction between the masses and the surfces is 0.25. The inclined plane makes an angle of `37^(@)` with the horizontal. If the mass `M_(1)`moves downwards with a uniform velocity, find (i) the mass of `M_(1)`, (ii) the tension in the horizontal portion. `(g=9.8 ms^(-2) , sin 37^(@)=(3)/(5))`

Text Solution

Verified by Experts

Let `T_(1)` be the tension in the string connecting `M_(1) and M_(2) and T_(2)` be the tension in the string connecting `M_(2) and M_(3)`. From the figure.

`M_(1)g=T_(1)`
`T_(2)=muM_(3)g=(0.25)4g`
Or, `T_(2)=g=9.8N`
Also
`T_(1)=T_(2)+(0.25)xx4g cos 37^(@) +4g sin37^(@)`
`=g(1+(4)/(5) +(4xx3)/(5))`
`T_(1)=(21)/(5)g`
Or, `M_(1)g=(21)/(5) g`
`therefore M_(1)=(21)/(5)=4.2 kg`
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