Question

In the adjoining figure block A is of mass $m$ and block B is of mass $2m$. The spring has force constant $k$. All the surfaces are smooth and the system is released from the rest with spring unstretched. Then:

• A. The maximum extension of the spring is $\frac{4mg}{k}$
• B. Tension in the thread for extension of $\frac{2mg}{k}$ in spring is $mg$
  
• C. Net acceleration of block B when the extension in the spring is maximum, is $\frac{2}{3}g$
• D. None of these

Answer 1

Answer: (A), (C)

The correct options are
A The maximum extension of the spring is $\frac{4mg}{k}$
C Net acceleration of block B when the extension in the spring is maximum, is $\frac{2}{3}g$

(a) Decrease in potential energy of B $=$ increase in spring potential energy

$\therefore 2mg{x}_m=\frac{1}{2}k{x}_m^2$

$\therefore x_m=\frac{4mg}{k}$

(b) $E_i=E_f$

$0=\frac{1}{2}(m+2m)v^2+\frac{1}{2}\times k\times \left({\frac{2mg}{k}}^2\right)-\left(2mg\right)\left(\frac{2mg}{k}\right)$

$\therefore v=2g\sqrt{\frac{m}{3k}}$

(c) $a=\frac{k{x}_m-2mg}{3m}$ (upwards)

$=\frac{k\left(\frac{4mg}{k}\right)-2mg}{3m}=\frac{2g}{3}$

(d) $T-2mg=ma$.....(i)

$2mg-T=2ma$.....(ii)

Solving these two equations, we get

$a=0$ and $T=2mg$