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

Explanation

On a rough horizontal plane, acceleration of a block of mass .m. is given by `a=(P)/(m)-mu_(k) g " "` ….(i)
Initially, `P =F , a=5 ms^(-2)`
`5=(F)/(10) mu_(k)(10) …..(ii) (because m = 10 kg)`
When force is doubled i.e., `P=2F , 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)rArr mu_(k)=(8)/(10)=0.8`