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A block of mass 10kg is pushed by a forc...

A block of mass `10kg` is pushed by a force `F` on a horizontal rough plane is moving with acceleration `5ms^(-2)` When force is doubled its acceleration becomes `18ms^(-2)` Find the coefficient of friction between the block and rough horizontal plane `(g =10ms^(-2))` .

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On a rough horizontal plane , acceleration of a block of mass 'm' is given by `a = (F)/(m) - mu_(k) g " " ….. `(i)
Initially , `" " a = 5 ms^(-2)`
`5= (F)/(10) - mu_(k)(10) ( because m = 10 kg) " " ..... `(ii)
When force is doubled `a = 18 ms^(-2)`
`18 = (2F)/(10) - mu_(k) (10) " " ....... `(iii)
Multiplying Eq. (ii) with 2 and subtracting from Eq.(iii)
`8 mu_(k) (10) implies mu_(k) = (8)/(10) = 0.8`
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