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Q.A block of mass M on a horizontal smooth surface is pulled by a load of mass M/2 by...

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user8235304 | Student, Grade 11 | Valedictorian

Posted July 7, 2013 at 1:45 AM via web

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Q.A block of mass M on a horizontal smooth surface is pulled by a load of mass M/2 by means of a rope AB and string BC as shown in figure.The length and mass of the rope AB are L and M/2 respectively.As the block is pulled from AB=L to AB=0;its acceleration changes from

A)   `(3g)/4` to `g`

B)    `g/4` to `g/2`

C)    `g/4` to `g`

D)   `(3g)/2` to `2g`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 7, 2013 at 2:08 AM (Answer #1)

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The mass of the block on the smooth horizontal surface is M. A load of mass `M/2` that is suspended on the side pulls the block. The load is attached to the block by a vertical string and a horizontal rope of length L and mass `M/2` .

There is a force `(M/2)*g` with which the load is pulled downwards; this accelerates the block. Initially, the load pulls the block as well as the attached rope. the total mass of the two is `M/2 + M = (3M)/2` . The mass of the block, the rope and the load is 2*M. When a force `(M/2)*g` acts on this the resulting acceleration is `((M/2)*g)/((3M)/2+M/2)` = `g/4` .

When the block moves to the edge of the surface, the rope is hanging down. A force equal to `(M/2 + M/2)*g` pulls the load and the rope downwards. This results in an acceleration of the block equal to `(M*g)/(2*M) = g/2`

The correct option is B, acceleration changes from `g/4` to `g/2` .

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