IITJEE.TK �MODEL PAPER
Physics Mains
Time : 120 min�������������������������������������������������������������������������������������������� ����������������������������������������������������������� ����������� ����������� ����������� Max: 120
1.
Two stones are thrown simultaneously from the same point
with an initial velocity of 20 m/s, one straight up �and the other at an angle of 300 to the horizontal.
Find the distance between the stones after 2 seconds.
2.
Three ships� A,B,C
are sailing at constant speeds on steady courses. B is sailing due east at
12kmph and C is sailing in a direction N300E at 8kmph. To an
observer on C, the direction of A appears to be S300E and to an
observer on B, A appears to be sailing due south. Find the speed of A and it
actual direction.
3.
A sphere of diameter d rolls on the inside surface of a
foxed hollow cylinder of radius R without slipping. Determine the frequency of
small rolling oscillations of sphere about the lowest point of the cylinder.
4.
Find the acceleration of the block of mass M in the
situation shown in the figure. The coefficient of friction between the two
blocks is n1 and that between the between the bigger block and the ground
is n2
5. Two men A and B each of
mass �m sit on loops at the ends of
a light flexible rope passing over a smooth pulley, A being h metres higher
than B. In B�s hand is placed a ball os mass m/10 which he instantly throws
up to A, so that it just reaches him. Calculate (a) The distance through
which A moves by the time he catches the ball. (b) The total distance moved
by A when he ceases to ascend. 6. Find the specific heat
capacities Cp and Cv for a gaseous mixture consisting
of 7g of nitrogen and 20g of argon. The gases are assumed to be ideal.
(� molecular mass of Nitrogen is 28
and that of Argon is 40) 7. A circular tube of
uniform bore is half filled with equal volumes of four liquids which do not
mix up and whose densities are in the ratio 1:4:8:7 and is held with its
plane vertical. Find the angle that the free surface makes with the
vertical. 8. A tuning fork of frequency
256 is moved towards a wall at a speed of 3m/s. An observer standing on the
side of the fork away from the wall hears two sounds, one directly from the
fork and the other reflected from the wall . How many beats per second will
be heard?Take the speed of sound in air as 340 m/s. 9. An insulated conductor
initially free from charge is replaced by repeated contacts with a plate
which after each contact is replenished with a charge Q (from an
electrophorous). If q is the charge on the conductor after the first
operation , find the maximum charge which can be given to the conductor in
this way. 10. A capacitor of capacitance
C1=1�F
withstands the maximum voltage� V1
=6kV while a capacitor� of
capacitance C2=2�F, the
maximum voltage V2=4kV. What voltage will the system of these
two capacitors withstand if they are connected in series. 11. An electron is released
from the origin at a place where a uniform electric field� E and a uniform magnetic field B exist
along the negative Y-axis and the negative Z-axis respectively. Find the
displacement of the electron along the Y-axis when its velocity becomes
perpendicular to the electric field for the first time. 12. Three particles each of
mass m are placed at the three corners of an equilateral triangle of side
a. Find the work to be done on this system to increase the sides of the
triangle to 2a.
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