Question

Initially the block of mass $m$ is in equilibrium in vertical plane (as shown) and there is a dielectric slab of some mass. When it is slightly displaced from its mean position :

Assume pulleys to be ideal and spring to be massless.

• A. dielectric will perform SHM having time period equal to $2\pi \sqrt{\frac{m}{k_s}}$
• B. dielectric will perform SHM having time period more than $2\pi \sqrt{\frac{m}{k_s}}$
• C. dielectric will perform SHM having time period less than $2\pi \sqrt{\frac{m}{k_s}}$
• D. dielectric will not perform periodic motion.

Answer 1

Answer: (A)

dielectric will perform SHM having time period equal to $2\pi \sqrt{\frac{m}{k_s}}$

Here the motion of the dielectric slab is same as the motion of mass m . The mass will perform SHM. i.e, $m\frac{d^{2}x}{d{t}^2}=-k_{s}x$

$\frac{d^{2}x}{d{t}^2}=-\frac{k_s}{m}x=-{\omega }^{2}x$

where, $\omega =\sqrt{\frac{k_s}{m}}$

$\Rightarrow \frac{2\pi }{T}=\sqrt{\frac{k_s}{m}},\Rightarrow T=2\pi \sqrt{\frac{m}{k_s}}$