Question

A bob of mass $2m$ hangs by a string attached to the block of mass $m$ of a spring block system. The whole arrangement is in a state of equilibrium. The bob of mass $2m$ is pulled down slowly by a distance $x_0$ and released

• A. For $x_0=\frac{3mg}{k}$ maximum tension in string is $4mg$
• B. For $x_0>\frac{3mg}{k}$, minimum tension in string is $mg$
• C. Frequency of oscillation of system is $\frac{1}{2\pi }\sqrt{\frac{k}{3m}}$, for all non-zero values of $x_0$
• D. The motion will remain simple harmonic for $x_0\le \frac{3mg}{k}$

Answer 1

Answer: (A), (D)

$kx=3mg;eq{u}^n.$
$k\left(x+x_0\right)-T-mg=ma$
$T-2mg=2ma$
On solving,
$T=\frac{2m}{3}k\left(x+x_0\right)$
$\therefore$ for $x_0=\frac{3mg}{k}$
$T=4mg$
(D) If $x_0=\frac{3mg}{k}$

If $x_0>\frac{3mg}{k}$ then string will become lack when ' $m$ ' comes to rest at top most extreme possible.]