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A block of weight 100N is pushed by a fo...

A block of weight 100N is pushed by a force F on a horizontal rough plane moves with an acceleration `1 m//s^(2)` , when force is doubled its acceleration becomes, `10 m//s^(2)` . The coefficient of friction is- (`g=10ms^(2)`)

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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 = 2 F , 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`
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