**
**Part A

1.Two liquids of masses
600 g and 500 g and densities 0.6 gcm^{-3} and
1.5 gcm^{-3} are combined to form a homogenous mixture. A
solid block of mass 420 g just floats in this mixture. Find the
density of the block material. If the equal volumes of the two liquids
were mixed instead, would this block float in that mixture? If it floats
find the fraction of the block that is visible above the mixture.

2.A lens of focal length f
produces an image of an object located 30 cm on one side of it at a
distance of 60 cm on the other side. If the lens is replaced by another of
3f/4, where would the image form? If the image has to form at the earlier
position by what distance should the object be shifted?

3.The devices D_{1} and D_{2}
shown (below left) are called diodes and have an interesting property.
When current flows in the direction of the arrow the resistance is low and
is called forward bias resistance. If the current were to flow in the
opposite direction the resistance is high and it is called reverse bias
resistance. For D_{1} forward bias resistance is 20 Ohm and
reverse bias resistance is 600 Ohm. For D_{2} forward bias
resistance is 30 Ohm and reverse bias resistance is 200 Ohm. Find the
equivalent resistance between A and B if (i) A is at a higher potential
(ii) B is at a higher potential

4.Rays of light are incident
symmetrically on a sphere of radius R as shown (below middle). Determine
the refractive index of the sphere material if they meet at P (You need to
write the correct expression for refractive index). Can the rays be made
to meet at C, the center of the sphere. If not, how should the rays be
incident to meet at C.

**
**Part B

7.Two candles of identical
lengths and different thicknesses were lit. Half of the thin candle and
one third of the thick candle could be seen to burn down in 15 minutes.
How long after the candles had been lit was the ratio of their lengths
4.

8.The average daily loss of
water of a human body is 0.8 kg, evaporated by the body. How much
food has to be consumed in order to compensate for the loss of energy
due to the evaporation if human body can use 70% of the energy provided
by the decomposition of food. The heat of combustion of food is
6,000 kJ/kg, the heat of vaporisation of water is 2440 kJ/kg

9.A train of length 300 m
passes through two tunnels with a gap of 400 m between them .The
tunnels are of length 800 m and 600 m respectively. From the
moment it just emerges from the first tunnel to the moment it just
disappears in to the second tunnel time elapsed is 60 s. Find the
time elapsed between the moments the train just enters the first tunnel
to the moment it just leaves the second tunnel.

10.Fiber optic cable of length
L has an inner core surrounded by an outer jacket. Light can travel
along the length of the cable through the inner and outer portions. The
refractive indices of the material of the inner and outer portions are m
_{1} and m _{2}. Find the
time interval between the moments when a light pulse entering one end of
the cable arrives at the other end traveling through the inner and outer
portions.

11.A person's heart does
approximately a work of 1.6 J during a beat. How much work does it
do during a day? By how much does the temperature of 10 kg of water rise
if it absorbs this much of energy?

12.Find the ratio E_{i}/E_{f},
where E_{i} and E_{f} are the energies of a neutron
before and after interaction with the nuclei of the moderator in a
nuclear reactor.

13.A stone projected vertically
upward on some planet reaches a maximum height h. Find the ratio of
times after projection when it is at a height of 5h/9.

14.A horizontal conductor is
oriented north south and carries some current. A positively charged
particle located vertically above it and having a velocity directed
northward experiences an upward force. What is the direction of the
force if this charged particle were located to the east of the conductor
and had a velocity directed towards the conductor.