A sonometer wire under suitable tension having specific gravity $$\rho$$, vibrates with frequency $$n$$ in air. If the load is completely immersed in water the frequency of vibration of wire will become

A radioactive nucleus emits $$4 \alpha$$-particles and $$7 \beta$$-particles in succession. The ratio of number of neutrons of that of protons, is [$$A=$$ mass number, $$Z=$$ atomic number]

A thin uniform rod has mass $$M$$ and length $$L$$ The moment of inertia about an axis perpendicular to it and passing through the point at a distance $$\frac{L}{3}$$ from one of its ends, will be

An obstacle is moving towards the source with velocity $$v$$. The sound is reflected from the obstacle. If $$c$$ is the speed of sound and $$\lambda$$ is the wavelength, then the wavelength of the reflected wave $$\lambda_r$$ is