Three blocks with masses $m$, $2m$, and $3m$ are connected by strings as shown in the figure. After an upward

Question

Three blocks with masses $m$, $2m$, and $3m$ are connected by strings as shown in the figure. After an upward force $F$ is applied on block $m$, the masses move upward at constant speed $v$. What is the net force on the block of mass $2m$? ($g$ is the acceleration due to gravity)

Accepted Answer

1. **Analyze Motion:** The problem states that the system of blocks moves upward with a **constant speed** $v$. Since the speed and direction are constant, the velocity is constant.
2. **Determine Acceleration:** According to the definition of acceleration ($a = \frac{dv}{dt}$), if velocity is constant, the acceleration is zero ($a = 0$) [NCERT Class 11, Physics Part I, Laws of Motion, Sec 4.5].
3. **Apply Newton's Second Law:** The net force acting on a body is given by the product of its mass and acceleration ($F_{net} = ma$).
4. **Calculate Net Force:** For the block of mass $2m$:
   $$ F_{net} = (2m) 	imes 0 = 0 $$
   The block is in dynamic equilibrium. This means the vector sum of all forces acting on it (tension from the upper string, tension from the lower string, and its own weight) is zero [NCERT Class 11, Physics Part I, Laws of Motion, Sec 4.8 Equilibrium of a Particle].

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