A time-dependent force F=3 t ( F in Newton and t in second)...

A time-dependent force $F=3 t$ ( $F$ in Newton and $t$ in second) acts on three blocks $m_{1}, m_{2}$ and $m_{3}$ kept in contact on a rough ground as shown. Co-efficient of friction between blocks and ground is $0.4 .$ If $m_{1}, m_{2}$ and $m_{3}$ are $3 \mathrm{~kg}, 2 \mathrm{~kg}$ and $1 \mathrm{~kg}$, respectively, the time after which the blocks started to move is $\left(g=10 \mathrm{~ms}^{-2}\right)$ (A) $4 \mathrm{~s}$ (B) $8 \mathrm{~s}$ (C) $\frac{8}{3} \mathrm{~s}$ (D) $\frac{4}{3} \mathrm{~s}$

A time-dependent force $F=3 t$ ( $F$ in Newton and $t$ in second) acts on three blocks $m_{1}, m_{2}$ and $m_{3}$ kept in contact on a rough ground as shown. Co-efficient of friction between blocks and ground is $0.4 .$ If $m_{1}, m_{2}$ and $m_{3}$ are $3 \mathrm{~kg}, 2 \mathrm{~kg}$ and $1 \mathrm{~kg}$, respectively, the time after which the blocks started to move is $\left(g=10 \mathrm{~ms}^{-2}\right)$
(A) $4 \mathrm{~s}$
(B) $8 \mathrm{~s}$
(C) $\frac{8}{3} \mathrm{~s}$
(D) $\frac{4}{3} \mathrm{~s}$

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Key Concepts

Newton's Second Law

Newton's second law is a fundamental principle of mechanics that relates the net force acting on an object to its mass and the acceleration produced. This concept is crucial for understanding how objects accelerate when forces—whether constant or variable in time—are applied, forming the basis for dynamic analysis in many physics problems.

Static Friction

Static friction is the resistive force that must be overcome to initiate the relative motion between two surfaces in contact. It depends on the coefficient of static friction and the normal force, and is central to problems involving the initiation of motion, as it determines the threshold force required to start movement.

Time-Dependent Force

A time-dependent force is one whose magnitude varies as a function of time. In dynamics, understanding how a varying force influences an object's motion over time is essential, particularly when determining critical moments—such as when a static system overcomes friction and begins to move.

Normal Force

The normal force is the perpendicular force exerted by a surface to support the weight of an object resting on it. It is a key factor in friction calculations, as it directly influences the maximum static friction that can be exerted between surfaces.

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