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Figure shows a light platform on which a...

Figure shows a light platform on which a man of mass M is standing and holding a string passing over a system of ideal pulleys. Another mass m is hanging as shown in fig. Find the force the man has to exert to maintain the equlibrium of system, and find the force exerted by the platform on the man. Also find the ratio of `M//m`.

Text Solution

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Let the man exertes force F on string
`2F=F+N+mg` ..(i)
and `F+N=Mg` ..(ii)

from eq. (i) and (ii): `F=((M+m)g)/(2) and N=((M-m)g)/(2)`

Also `N=3mg` …(iii)
For the whole system of (man + block +pulley)
`2F=Mg+mg` ...(iv)
From (i) and (iii) `F=4mg`, also we can get `M=7m`.
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