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Two blocks of masses 5kg and 10kg are at...

Two blocks of masses 5kg and 10kg are attached with the help of light string and placed on a rough incline as shown in the figure. Coefficients of friction are as marked in the figure. The system is released from rest. Determine the acceleration of the two blocks.

Text Solution

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Let 10kg block is sliding down, then acceleration of both the bloks are given by,
`a = ( 10g sin 37^(@) - mu_(1) xx 10 g cos 37^(@) - 5 g sin50^(@) -mu_(2) xx 5 g cos 50^(@))/(15) = -ve`
It means our assumed direction of motion is wrong and 5 kg block is going to slide down, if this would be the case, the direction of friction force will reverse and acceleration of blocks would be given by `:`
`a_(1) = ( 5 g sin 50^(@) - mu_(2) xx 5 g cos 50^(@) -mu_(1) x 10g cos 37^(@) - 10 g sin 37^(@))/( 15) = - ve `
It means in this direction also there is no motion. So we can conclude that the system remains at rest and friction force is static in nature.
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