In figure $m_{1} = 1 k g$ and $m_{2} = 4 k g$ . Find the mass $M$ of the hanging block which will prevent the smaller block from slipping over the triangular block. All the surfaces are frictionless and the strings and the pulleys are light.

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Solution

As the block 'm' does not slinover M'. ct will have same acceleration as that of M'
From the freebody diagrams.
$T + M a - M g = 0$ ...(i) (From FBD - 1)
$T - M^{'} a - R sin θ = 0$ ...(ii) (FRom FBD - 2)
$R sin θ - m a = 0$ ...(iii) (From FBD - 3)
$R cos θ - m g = 0$ ...(iv) (From FBD - 4)$

Eliminating T.R and a from above equation, we get $M = \frac{M^{'} + m}{cot θ - 1}$

This is the required mass of the hanging block

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In figure m1=1kg and m2=4kg. Find the mass Mof the hanging block which will prevent the smaller block from slipping over the triangular block. All the surfaces are frictionless and the strings and the pulleys are light.

In figure $m_{1} = 1 k g$ and $m_{2} = 4 k g$ . Find the mass $M$ of the hanging block which will prevent the smaller block from slipping over the triangular block. All the surfaces are frictionless and the strings and the pulleys are light.