Three boys step off together from the same spot. Their steps measure 63 cm, 70 cm and 77 cm respectively. What is the minimum distance each should cover so that all can over the distance in complete steps ?

A convex and concave lens having focal lengths of 30 cm and j10 cm respectively are placed at a distance 20 cm from each other.Whre should a source of light be placed so that the system of the two lenses will produce a beam of parallel rays?

An air capacitor has plates of 6 cm diameter. At what distance should the plates be placed so as to have the same capacitance as a sphere of diameter of 90 cm?

Two equal magnetic poles placed 25 cm apart in air exert a fore o 4xx10^-3N on each other. What should be the distance between them, so that force exerted by them on each other becomes 0.1 N?

The human eye has an approximate angular resolution of phi=5.8 xx 10^-4 rad and a typical photoprinter prints a minimum of 300 dpi (dots per inch, 1 inch = 2.54 cm). At what minimal distance z should a printed page be held so that one does not see the individual dots.

A convex lens of power 4D is placed at a distance of 40 cm from a wall at what distance from the lens should a candle be placed so that its image is formed on the wall?

A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index of water? If water is replaced by a liquid of refractive index 1.63 up to the same height, by what distance would the microscope have to be moved to focus on the needle again?

A man with normal near point (25 cm) reads a book with small print using a magnifying glass: a thin convex lens of focal length 5 cm- What is the closest and the farthest distance at which he should keep the lens from the page so that he can read the book when viewing through the magnifying glass?

At what distance should be placed from a convex lens of focal length 15 cm to obtain an image three times the size of the object?

A square sheet of tin of side 36 cm is to be made into a box without top by cutting off squares from each comer and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is maximum ?