Question

In figure (A), mass ‘2 m‘ is fixed on mass ‘m‘, which is attached to two springs of spring constant k. In figure (B), mass ‘m‘ is attached to two springs of spring constant ‘k‘ and ‘2k‘. If mass ‘m‘ in (A) and in (B) are displaced by distance’ x’ horizontally and then released, then time period T1 and T2 corresponding to (A) and (B) respectively follow the relation.

• A. $\frac{T_1}{T_2}=\frac{3}{\sqrt2}$
• B. $\frac{T_1}{T_2}=\sqrt{\frac{3}{2}}$
• C. $\frac{T_1}{T_2}=\sqrt{\frac{2}{3}}$
• D. $\frac{T_1}{T_2}=\frac{\sqrt2}{3}$

Answer 1

Answer: (A)

$\frac{T_1}{T_2}=\frac{3}{\sqrt2}$

Answer 2

Both the springs are in parallel combination in both the diagrams so
T1=2π$2\pi\sqrt{\frac{3m}{2}}$k and T2=2π $\sqrt{\frac{M}{3k}}$
So, $\frac{T_1}{T_2}=\frac{3}{\sqrt2}$