A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.

A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from the base of the wall.

In a double slit interference experiment, the separation between the slits is 1.0 mm, the wavelength of light used is 5.0 x 10^ -7 m and the distance of the screen from the slits is 1.0 m. (a) Find the distance of the centre of the first minimum from the centre of the central maximum. (b) How many bright fringes are formed in one centimeter width on the screen ?

A small piece of cesium metal phi=1.9eV is kept at a distance of 20 cm form a large metal plate having a charge density of 1.0xx 10^-9 C m^-2 on the surface facing the cesium piece. A monochromatic light of wavelength 400nm is incident on the cesium piece. Find the minimum and the maximum kinetic energy of the photoelectrons reaching the large metal plate. Neglect any change in electric field due to the small piece of cesium present.

A cylindrical tank of height 0.4m is open at the top and has a diameter 0.16m. Water is filled in it uo to height of 0.16m. Find the time taken to empty the tank through a hole of radius 5xx10^(-3)m in its bottom.

A totally reflecting, small plane mirror placed horizontally faces a parallel beam of lighy as shown in figure. The mass of the mirror is 20g. Assume that there is no absorption in the lens and that 30% of the light emitted by the source goes through the lens. Find the power of the source needed to support the weight of the mirror. Take g= 10 m s^-2.

Find the area of four walls of a room (Assume that there are no doors or windows ) if its length 12m. Breadth 10 m. and height 7.5 m.

A point source emitting alpha particles is placed at a distance of 1 m from a counter which records any alpha particle falling on its 1 cm^2 window. If the source contains 6.0xx10^16 active nuclei and the counter records a rate of 50000 counts//second, find the decay constant. Assume that the source emits alpha particles fall nearly normally on the window.