Two travelling waves produces a standing wave represented by equation,

y = 1.0 mm cos(1.57 cm^$$-$$1) x sin(78.5 s^$$-$$1)t.

The node closest to the origin in the region x > 0 will be at x = .............. cm.

White light is passed through a double slit and interference is observed on a screen 1.5 m away. The separation between the slits is 0.3 mm. The first violet and red fringes are formed 2.0 mm and 3.5 mm away from the central white fringes. the difference in wavelengths of red and violet light is ................ nm.

Consider a badminton racket with length scales as shown in the figure.


If the mass of the linear and circular portions of the badminton racket are same (M) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, $${r \over 2}$$ distance from the end A of the handle will be ................ Mr².