A box of mass m , kg is placed on the rear si | vedclass

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(D) To find the net acceleration of the box with respect to the truck,we analyze the forces acting on the box in the non-inertial frame of the truck.$

Vedclass · Accepted Answer

It could be any value

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(D) To find the net acceleration of the box with respect to the truck,we analyze the forces acting on the box in the non-inertial frame of the truck.$1$. The truck is accelerating forward with $a = 4 \, m/s^2$.$2$. $A$ pseudo force $F_p = ma$ acts on the box in the backward direction.$3$. The frictional force $f$ acts in the forward direction to oppose the motion,where $f = \mu N = \mu mg$.$4$. For the box to have zero acceleration with respect to the truck,the pseudo force must be balanced by the frictional force:$ma = \mu mg$$a = \mu g$$5$. Substituting the given values:$4 = 0.4 	imes 10$$4 = 4$Since the mass $m$ cancels out from both sides of the equation,the condition for zero relative acceleration is independent of the mass of the box.Therefore,the box will remain stationary with respect to the truck for any value of $m$.

$A$ box of mass $m \, kg$ is placed on the rear side of an open truck accelerating at $4 \, m/s^2$. The coefficient of friction between the box and the surface below it is $0.4$. The net acceleration of the box with respect to the truck is zero. The value of $m$ is :- $[g = 10 \, m/s^2]$

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