Two simple harmonic motions are represented by equations $y_1=0.5 \sin \left[200 \pi \mathrm{t}+\frac{\pi}{3}\right]$ and $y_1=0.5 \cos \pi \mathrm{t}$. The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is :

A vertical spring of spring constant $24 \mathrm{Nm}^{-1}$ is fixed on a table. A ball of mass 0.5 kg at a height 2 m above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance of 50 cm . The net work done in the process is:

A sonometer string vibrates with a frequency of 400 Hz . When the length of the string is halved and the tension is altered, it begins to vibrate with a frequency of 200 Hz . The ratio of the new tension to the original tension in the string is:

In an experiment to measure the density of the material of a sphere, an error of $2 \%$ occurred while measuring the radius of a sphere and an error of $3 \%$ occurred while measuring the mass of the sphere. What is the maximum percentage error in the measurement of density?