Question

Two bodies of masses $m_1$ and $m_2$ connected by an ideal massless spring of stiffness $K$. The co-efficient of friction between the bodies and surface is $\mu$. The minimum force required to shift the body $m_2$ is $F$. Then -

• A. $m_1$ will first accelerate then decelerate
• B. $m_1$ will first accelerate upto a maximum velocity and then decelerate.
• C. $m_1$ will accelerate continuously
• D. both $\left(a\right)$ and $\left(b\right)$ are correct

Answer 1

The correct option is D both $\left(a\right)$ and $\left(b\right)$ are correct


If $m_1$ is pushed to right by $F$, then first spring will start compressing and spring force $\left(F_s\right)$ will act on $m_1$ towards left. Also, friction $f$ on it will act to the left with constant value.

As spring get compressed more, the $F_s$ will become stronger and stronger. After a while it will balance $F$. When $F_{net}=0$ on $m_1$, it will be in to have maximum velocity and will compress the spring more so, it will be retarded by $F_s$.