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A block of mass M is using on a rough ho...

A block of mass M is using on a rough horizontal surface. `mu_R` is the coefficient of kinetic friction between the block and the surface. What is the net force exerted by the surface on the block?

A

Mg

B

`muMg`

C

`Mgsqrt(1+mu_(K)^(2))`

D

`Mgsqrt(1-mu_(K)^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C

When the block is moving on the rough surface, it produces two forces on the block
(i) Normal reaction R=Mg and
(ii) The frictional force `f=muR=mu_kMg`
As these forces are perpendicular to each other, the resultant force,
`F=sqrt((Mg)^2+(mu_KMg)^2)=sqrt(M^2g^2(1+mu_K^2)`
`:." "F=Mgsqrt(1+mu_K^2)`
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