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Two blocks of masses 50 kg and 30 kg con...

Two blocks of masses 50 kg and 30 kg connected by a massless string pass over a light frictionless pulley and rest on two smooth planes inclined at angles `30^(@)` and `60^(@)` resp . With horizontal .Determine the accelertion in the two blocks and tension in the string `g = 10 m//s^(2)` .

Text Solution

Verified by Experts

The correct Answer is:
2.44
Suppose the mass of 50 kg slides down with an acceleration a. The forces acting on the two blocks are shown in figure. The components of the two weights perpendicular to the inclined planes are balanced by the normal reactions `R_(1)` and `R_(2)`

The tension T of each part of the string is same and also the acceleration a of each block is same.
`therefore 50g sin 30^(@) - T = 50 a`......... (i)
Adding `T - 30g sin 60^(@) = 30 a`..... (ii)
Adding (i) and (ii), we get
`(50 sin 30^(@) - 30 sin 60^(@))g = (50 + 30) a`
or `a = ((50 xx 0.5 - 30 xx 0.86) xx 10)/80 = -0.12 ms^(-2)`
From (i), `T = 50 g sin 30^(@) - 50 a`
`=50 (10 xx 0.5 - 0.12)`
`= 50 xx 4.88 = 2.44 N`
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