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))` .

Explanation

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