Question

In the figure shown the block of mass m is in equilibrium initially. Now the block is pushed down by a slight distance and released. (springs are identical and massless having spring constant k) Then

• A. Initial elongation of the spring is $\frac{mg}{2kcos\theta }$
• B. Initial elongation of the spring is $\frac{mg}{2kco{s}^2\theta }$
• C. Time period of oscillation of the block is $2\pi \sqrt{\frac{m}{2kco{s}^2\theta }}$
• D. Time period of oscillation of the block is $2\pi \sqrt{\frac{m}{2k}}.$

Answer 1

Answer: (A), (C)

The correct options are
A Initial elongation of the spring is $\frac{mg}{2kcos\theta }$
C Time period of oscillation of the block is $2\pi \sqrt{\frac{m}{2kco{s}^2\theta }}$

$2k{x}_{0}cos\theta =mg\dots \left(i\right)$

$F_R=-2Kco{s}^2\theta x$

$\omega =\sqrt{\frac{2Kco{s}^2\theta }{m}}$

$\therefore \left(A\right)and\left(C\right)$