12 th IIT 21 st May Test Solution 101, Blue Diamond Complex, Fatehgunj, Vadodara-02 .Tel. No. 2787268 / 2750018 / 2782232 2 Subject-PHYSICS Part : 1 SECTION-A (NEXT EIGHT QUESTIONS: SINGLE CHOICE – ONLY ONE CORRECT ANSWER) Q1 The electric field in a region (relative permittivity = 1) varies with distance “r” from origin according to relation , ˆ 2 r Ar E where A is a positive constant. The volume charge density in the region is proportional to (a.) r (b.) 2 r (c.) r / 1 (d.) 2 / 1 r Sol. (a) dx x x r K Q r K Ar E r 2 0 2 2 2 4 ) ( [where Q is total charge inside sphere of radius ]. r dx x r r 0 2 4 x Q2 A solid hemispherical uniform charged body having charge Q is kept symmetrically along the y-axis as shown in figure. The electric potential at a distance d from the origin along the x -axis at point P will be (a.) d Q 0 4 1 (b.) Less than d Q 0 4 1 (c.) More than d Q 0 4 1 and less than d Q 0 4 2 (d.) More than d Q 0 4 2 Sol. (a) By symmetry, potential at P is same due to upper & lower half Q3 A steel block of mass M is being lifted by a helicopter, which is accelerating upward with an acceleration of magnitude a. The block is attached to a horizontal bar by two cables, which make angles of θ 1 and θ 2 w.r.t. horizontal as shown in the figure. The tension in the cable 1 in terms of M, θ 1 , θ 2 , g and a is
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12th IIT 21st May Test Paper - Solution - YLCeducation.ylc.co.in/.../08/12th-IIT-21st-May-Test-Paper-Solution.pdf · M g a Q4 A block of mass 1 kg is kept over another block of plane.
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Q8 A water cooler of storage capacity 120 litres can cool water at constant rate of P watts. In a closed circulation
system (as shown schematically in the figure), the water from the cooler is used to cool an external device that
generates constantly kW3 of heat (thermal load). The temperature of water fed into the device cannot exceed
C30 and the entire stored 120 litres of water is initially cooled to C.10 The entire system is thermally
insulated. The minimum value of P (in watts) for which the device can be operated for 3 hours is:
(Specific heat of water is 11KkgkJ4.2 and the density of water is 3mkg1000 )
(a.) 1600 (b.) 2067 (c.) 2533 (d.) 3933
Sol. (b)
SECTION-B
(MULTIPLE CHOICE – ONE OR MORE THAN ONE CORRECT ANSWER)
Q1 In the presence of stationary charges in the space, line integral of the electric field
dE for a closed path as
shown, is carried out:
(a.) The value of the integral is independent of the path (b.) The value of the integral is independent of where charges may be located relative to the path (c.) The value of the integral is always is constant (d.) The value of the integrals is always negative
Q2 The figure shows, two point charges )0(2 Q and .Q The charges divide the line joining them in three
parts I, II and III
(a.) Region III has a local maxima of electric field (b.) Region I has a local minima of electric field
(c.) Equilibrium position for a test charge lies in region II (d.) Region II has a local minima of electric field
Sol. (a, d)
Q3 A particle A moves with a velocity 1v and a particle B moves with a velocity ,2v w.r.t. ground
and r is the length of the vector, ,AB then
(a.) 0
dtdr
if |||| 12 vv
(b.) 0
dtdr
if |||| 12 vv
(c.) 0
dtdr
if ABvABv .. 12
(d.)
0dtdr
if 0.)( 21 BAvv
Sol. (c, d)
ABuvvdtdr .)( 12 where ABu is a unit vector along AB
Q4 Two blocks of masses m2 and m are connected as shown in the figure. Now the string between the blocks is
suddenly broken.
(a.) gaA (b.)
2gaA
(c.) gaB (d.)
2gaB
Sol. (b, c) ‘B’ is in free fall, as string is cut, hence gaB tension in string, before it is cut, is Mg. hence net force on A
after cutting string is Mg 2gaA
Q5 A ball tied to the end of a string swings in a vertical circle under the influence of gravity (a.) When the string makes an angle 90 with the vertical the tangential acceleration is zero and radial acceleration
is somewhere between maximum and minimum (b.) When the string makes an angle 90 with the vertical the tangential acceleration is maximum and radial
acceleration is somewhere between maximum and minimum (c.) At no place in the circular motion, tangential acceleration is equal to radial acceleration in magnitude (d.) Throughout the path whenever radial acceleration has its extreme value, the tangential acceleration is zero
Sol. (b, d) In the shown diagram at position A and C radial acceleration has its maximum values and there
is no component of acceleration in tangential direction.
At position B and D tangential acceleration is maximum )(g and radial acceleration in some
where between maximum and minimum. Q6 Bodies of mass 0.5 kg resting on a horizontal frictionless tabletop are connected with an unstretched spring of
length L = 20 cm and of spring constant 16 N/m. The mass of the spring is negligible. At a certain moment the
bodies are given an initial speed of 0v = 0.36 m/s towards the wall on the right. The body at the right collides
with the wall totally elastically
(a.) There will be 2 collisions with the wall (b.) After 1st collision centre of mass comes to rest (c.) After 2nd collision centre of mass moves to left with speed v0 (d.) After all collisions are over, the system oscillates about the centre of mass
Sol. (a, b, c)
After 1st collision two are moving with speeds 0v in opposite direction. Hence centre of mass is at rest & two
start oscillating with initial position as mean position. So mass on right again collides with wall when at mean
position & both masses have same speed towards left after collision.
SECTION-D
Integer Answer Type
This section Contains 6 questions. The answer to each of the questions is a single digit integer, ranging from 00 to
99. The appropriate bubbles below the respective question numbers in the OMR have to be darkened.
Q1 A tank is filled upto a height 10 m with a liquid and is placed on a platform of height 2m from the ground. The
distance h from the ground where a small hole should be punched so that the liquid stream coming out of the
hole covers maximum horizontal distance in meters is
(b.) The equilibrium constant should be lower than one for the above reaction (c.) C)(CD 33 will be more stable than C)(CH 33 due to higher electron releasing nature of deuterium than
hydrogen (d.) C)(CD 33 will be more stable than C)(CH 33 due to presence of stronger DC bond than HC bond
Sol. (a) cCH 33 )( is more stable than CCD
3)3( due to weaker bond strength of C-H bond
Q6 If the speed of electron in first Bohr orbit of hydrogen be ‘x’, then speed of the electron in second orbit of He+
is: (a.) x / 2 (b.) 2x (c.) x (d.) 4x
Sol. nZV
nZVH
1x
22
HeV
1HeV
1HeV
x xVHe
Q7 The molar entropy of vaporization of acetic acid is 14.4 cal K–1 mol–1 at its boiling point C.118 The latent
heat of vaporization of acetic acid is
(a.) 49 cal g–1 (b.) 64 cal g–1 (c.) 94 cal g–1 (d.) 84 cal g–1
Q8 The crystal system of a compound with unit cell dimensions nm504.0,387.0,387.0 cba and
(MULTIPLE CHOICE – ONE OR MORE THAN ONE CORRECT ANSWER)
Q1 Three metals of alkaline earth metal group (A, B and C) when reacted with a fixed volume of liquid bromine separately gave product (metal bromide) whose mass is plotted against mass of metals taken as shown in the figure: