Question

In the figure shown masses of the blocks $A$, $B$, and $C$ are $6kg$, $2kg$, and $1kg$ respectively. Mass of the spring is negligibly small and its stiffness is $1000N/m$. The coefficient of friction between the block $A$ and the table is $\mu =\mathrm{0.8.}$ Initially, block $C$ is held such that spring is in a relaxed position. The block is released from rest. Find: $(g=10m/s^2)$ the maximum distance moved by the block $C$.

• A. $2\times {10}^{-2}m$
• B. $3\times {10}^{-2}m$
• C. $4\times {10}^{-2}m$
• D. $6\times {10}^{-2}m$

Answer 1

The correct option is A $2\times {10}^{-2}m$

Equilibrium position for block $C$ is at a distance $x=mg/k$ distance below the initial point. $x=0.01m$. If the block $A$ doesn't move then the maximum distance $C$ can move down is $0.02m$ under SHM. When $C$ is moved to maximum distance then the tension in the spring is $1000$ x $0.02N=20N$.

If block $A$ didn't move then block $B$ also didn't move, thus

$mg+k{x}_2-T=0,$ where $T$ is the tension in the string and $x_2$ is elongation in the spring.

$T=mg+k{x}_2=20+20=40N$

For block $A$, maximum static friction is $\mu m_{A}g=48N,$ thus block $A$ won't move and maximum displacement of the block $C$ is $20cm.$