A simple harmonic progressive wave is given by $$Y=Y_0 \sin 2 \pi\left(n t-\frac{x}{\lambda}\right)$$. If the wave velocity is $$\left(\frac{1}{8}\right)^{\text {th }}$$ the maximum particle velocity then the wavelength is

In a meter bridge experiment, the balance point is obtained at length $$\ell_1 \mathrm{~cm}$$ from left end when resistances in the left gap and right gap are $$5 \Omega$$ and $$R \Omega$$ respectively. When the resistance $$R$$ is shunted with equal resistance, the new balance point is at $$1.6 \ell_1$$. The resitance $$R$$ in ohm is

In the graphical representation of e.m.f. '$$\mathrm{e}$$' and current '$$\mathrm{i}$$' versus '$$\omega \mathrm{t}$$' for an a.c. circuit, both emf and current reach zero, minimum and maximum value at the same time. The circuit element connected to the source will be

The moment of inertia of a body about a given axis is $$1.2 \mathrm{~kg} / \mathrm{m}^3$$. Initially the body is at rest. In order to produce rotational kinetic energy of $$1500 \mathrm{~J}$$, an angular acceleration of $$25 \mathrm{rad} / \mathrm{s}^2$$ must be applied about an axis for a time duration of