|Time: ONE Hour||
Max. Marks: 60
Two small stones are tied at the ends of a rope of length 5
m . Imagine you are holding them, one in each hand, with the rope hanging
loosely on the top floor balcony of a tall building. You release one stone at
a certain moment and the other 0.5 s later along the same vertical line from
the same position. The rope will be taut after a time of .
Assume that as the rope gets taut, the velocities of the stones becomes equal
to the average of the velocities of the stones just before the stone gets
taut. The velocities of the stones 2 s later would be .
A concave mirror of focal length 25 cm and a convex lens of focal length 20 cm are arranged coaxially 85 cm apart. A point object is located on the principal axis of the system 30 cm from the convex lens. Rays of light after passing through the lens fall on the mirror and after reflection from the mirror pass through the lens again. These rays converge at a distance of from the lens after passing through it a second time.
A cylindrical wire of radius R is made of two different
materials. The inner portion of radius R/2 is made of a material of
resistivity r and the outer annular portion of
thickness R/2 is made of material of resistivity 2r
. Resistance per unit length of this wire would be .
A boat moves down stream a certain distance in a river. If the river were not flowing the time taken would have been 2 hrs but with the river flowing the time taken is 1.5 hrs. The time taken to travel upstream the same distance would be .
Imagine a man moving from north
pole to the equator and from the equator to the south pole, moving along the
same longitude. The magnitude of the displacement in the first and second parts
are _____________ and ______________ and the total displacement is
A chain is lying as a heap on a table. One end of it is
pulled vertically upward with a constant acceleration of 0.5 m/s2.
The velocity of the mid point of the vertical portion when the upper end is at
height of 0.64 m above the table is .
A carom striker hits a side of the carom board at some angle and rebounds. It then hits the adjacent side. The angle between the initial and final directions of motion is ____________. (Assume the angles made by the line of motion with the normal before and after collision are same for both the collisions)
A sphere consists of inner portion of radius r made of a material of density 8 gm/cm3 , and an outer layer of thickness t made of a material of density 4 gm/cm3. This sphere floats in a liquid of density 10 gm/cm3 with half its volume submerged. The ratio r/t is equal to _____________________.
Sound wave of a frequency n travels in a certain gaseous
medium with a velocity v. A second gaseous medium at same pressure as the
first has twice greater density. The speed of sound of frequency 2n in this
medium would be
A radio active substance of half life period 2 hrs is being
produced in a reactor. At the initial moment the mass of the substance is zero
and production rate is 5 mg/s. The substance is produced for 10 s. Two hours
later the mass of the radioactive substance would be nearly .
A negatively charged particle moving at right angles to a
magnetic field in the southeast direction experiences a vertical upward force.
The force experienced by a positively charged particle moving in the northwest
direction would be .
Energy released in a fusion reaction of two Deuterons is nearly 24 MeV. Energy released in the fission of U235 is nearly 200 MeV. The mass of Uranium that should undergo fission to release the same amount of energy as obtained by fusing nuclei contained in 1 kg Deuterons would be and the energy released is .