1. A transverse harmonic disturbance is produced in a string. The maximum transverse velocity is 3 m/s and maximum transverse acceleration is 90 m/s². If the wave velocity is 20 m/s then find the waveform.
2. A cylinder of mass m and radius R rolls down an inclined plane of inclination θ. Calculate the linear acceleration of the axis of cylinder.
3. A long solenoid of radius a and number of turns per unit length n is enclosed by cylindrical shell of radius R, thickness d (d is very small compared to R) and length L. A variable current i = i0sin ωt flows through the coil. If the resistivity of the material of cylindrical shell is ρ, find the induced current in the shell.
Highly energetic electrons are bombarded on a target of an element containing 30 neutrons. The ratio of radii of nucleus to that of Helium nucleus is (14)1/3.
4. Find atomic number of the nucleus.
5. Find the frequency of Kα line of the X−ray produced. (R = 1.1 × 107 m-1 and c = 3 ×108 m/s)
Source 2005 JEE Main