Question

A bob of mass $2 m$ 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 $2 m$ is pulled down slowly by a distance $x _{0}$ and released

• A. For $x _{0}=\frac{3 mg }{ k }$ maximum tension in string is $4 mg$
• B. For $x_{0}>\frac{3 m g}{k}$, minimum tension in string is $m g$
• C. Frequency of oscillation of system is $\frac{1}{2 \pi} \sqrt{\frac{ k }{3 m }}$, for all non-zero values of $x_0$
• D. The motion will remain simple harmonic for $x _{0} \leq \frac{3 mg }{ k }$

Answer 1

Answer: (A), (D)

$kx =3 \,mg ; equ ^{ n } .$
$k \left( x + x _{0}\right)- T - mg = ma$
$T -2 mg =2 ma$
On solving,
$T =\frac{2 m }{3} k \left( x + x _{0}\right)$
$\therefore $ for $ x _{0}=\frac{3 mg }{ k } $
$ T =4 mg$
(D) If $x_{0}=\frac{3 m g}{k}$

If $x_{0} > \frac{3 mg }{ k }$ then string will become lack when ' $m$ ' comes to rest at top most extreme possible.]