Question

A block of mass $0.2kg$, which slides without friction on a ${30}^{\circ }$ incline is connected to the top of the incline by a mass less spring of force constant $80N/m$ as shown in the figure. If the block is pulled slightly from its mean position, what is the period of oscillations?

• A. $\pi sec$
• B. $\frac{\pi }{10}sec$
• C. $\frac{2\pi }{5}sec$
• D. $\frac{\pi }{2}sec$

Answer 1

The correct option is B $\frac{\pi }{10}sec$

Here the block will perform SHM.

Thus, $F=-kx$
or $ma=-kx$ or $a=-\left(k/m\right)x$
Thus, angular frequency $\omega =\sqrt{\frac{k}{m}}=\sqrt{\frac{80}{0.2}}=20$
Time period $T=\frac{2\pi }{\omega }=\frac{2\pi }{20}=\frac{\pi }{10}$ sec.