$A$ body of mass $200\,g$ is tied to a spring of spring constant $12.5\,N/m$,while the other end of the spring is fixed at point $O$. If the body moves about $O$ in a circular path on a smooth horizontal surface with a constant angular speed of $5\,rad/s$,then the ratio of the extension in the spring to its natural length will be:

Two simple harmonic motions are represented by the equations $y_1 = 0.1 \sin(100\pi t + \frac{\pi}{3})$ and $y_2 = 0.1 \cos(100\pi t)$. The phase difference of the velocity of particle $1$ with respect to the velocity of particle $2$ is

$\lim _{x \rightarrow 0} \left( \frac{x \cdot 10^x - x}{1 - \cos x} \right)$ is equal to

The maximum energy in the thermal radiation from a hot source occurs at a wavelength of $11 \times 10^{-5} \text{ cm}$. According to Wien's displacement law,the temperature of the source (on the Kelvin scale) will be $n$ times the temperature of another source (on the Kelvin scale) for which the wavelength at maximum energy is $5.5 \times 10^{-5} \text{ cm}$. The value of $n$ is:

Identify the plant shown in the given figure.

Which part of the cauliflower is used as a vegetable?