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Question

A block is projected along a rough horizontal surface with a velocity of 5 m/s. If the block comes to rest after travelling a distance of 4 m, then the coefficient of kinetic friction is (Take g=10 m/s2)

A
0.25
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B
0.31
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C
0.21
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D
0.20
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Solution

The correct option is B 0.31
Let the mass of the block be m. Kinetic friction f will be acting in the direction opposite to the velocity of the block.
Friction acts as a decelerating force on the block.
Friction force f=μkN=μkmg
Taking direction of initial velocity as +ve direction,
a=fm=μkg ...(i)


Distance travelled by block before coming to rest is 4 m.
Applying kinematic equation, v2=u2+2as ...(ii)
where v=0, u=+5 m/s
a=μkg m/s2, s=+4 m
Putting all values in Eq. (ii),
0(5)2=2×4×(μkg)
25=8μkg
μk=258×10=0.31
Hence, option (b) is correct.

Alternate solution :

Using work energy theorem we can say that :
Work done by all forces = change in kinetic energy
Here, work is done by friction force only.
W=ΔK.E.
fs=12mu2
( work done by friction is negative and final velocity of block is zero)
μkmg×4=12mu2
μk=5240×2
μk=0.31

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