
A car traveling at a certain
speed v_{1} overtakes another car traveling at a slower speed v_{2}
at A. An hour later the faster car reverses
its direction, changes it’s speed to v_{3} and after some time meets
the slower car now coming in the opposite direction at position B. The distance
between the positions A and B is 10 km. Find the speed of the slower car if v_{1}  v_{2} = v_{3}
+ v_{2}. Find the value of v_{2}.

Two lenses of focal
lengths f_{1} and f_{2} kept in contact can be replaced by a
single lens of focal length f. This focal length is given by the following
formula
In using this formula the focal length of a convex lens is
taken as positive and the focal length of a concave lens is taken as negative.
Use this formula to solve the following problem.
A point object is placed 36 cm away from a convex lens and
its image is formed on a screen placed 180 cm away from the lens on the
other side. If now a second lens is placed in contact with the first lens, the
screen has to be shifted by 90 cm towards the lenses in order to obtain a clear
image on it. What is focal length of the second lens? The screen is fixed at
this position now and the focal length of the second lens is doubled. Find the
distance through which the object has to be shifted to obtain a clear image on
the screen.

Three conducting wires
of equal radii having lengths in the ratio 1:2:3 have their resistivities in the
ratio 2:3:4. These wires are connected end to end. When a certain potential
difference is applied between the free ends of the combination, potential
difference between the ends of middle conductor is found to be 60 V. Find the
potential differences between the ends of the other conductors. If the rate of
heat production from the first conductor is 4 W, find the rate of heat
production from the other two.

Two cubes made of same
material have some hollow space in them and are floating in a liquid of density
2 g/cm^{3}. One cube is just floating while the other has three fourths
of its volume below water. If the cavities in the cubes have their volumes in
the ratio 1:2 find the density of the material of the cube.

A long horizontal
conductor carrying a current is oriented along east west line. An electron
located above the conductor and moving eastward experiences a force towards the
conductor. Another electron located vertically below the conductor has its
velocity directed towards the conductor. Find the direction of force on this
electron.