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A body of mass 4kg is kept on the base of a truck. Coefficient of static and kinetic frictions between the body and the truck are 0.6 and 0.2. The truck is kept on a perfectly smooth surface. $(g = 10 {ms}^{2})$
Statement A: If the truck is subjected to an acceleration of 3ms^-2 , frictional force between the body and the truck is 12N.
Statement B: If the truck is subjected to an acceleration of 8ms^-2 , frictional force between the body and the truck is 8N.

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Both the statements A & B are correct

Both the statements A&B are wrong

Statement A alone is correct

Statement B alone is correct

answer is A.

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Detailed Solution

$f_{L} = μ_{s} mg = 0.6 \times 4 \times 10 = 24 N$

$f_{k} = μ_{k} mg = 0.2 \times 4 \times 10 = 8 N$

If, $a_{truck} = 3 {ms}^{- 2}$

Pseudo force on the block,

$F_{A} = {ma}_{truck} = 4 \times 3 = 12 N$

$∵ F_{A} < f_{L}$

$∴ friction = f_{s} = F_{A} = 12 N$

If, $a_{truck} = 8 {ms}^{- 2}$

Pseudo force on the block,

$F_{B} = {ma}_{truck} = 4 \times 8 = 24 N$

$∵ F_{B} > f_{L}$

$∴ friciton = f_{k} = 8 N$

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