JEE is an examination conducted for admission into some of the reputed organisations across the country. The examination is conducted in two levels - JEE Main and JEE Advanced. The subjects for the engineering entrance tests are Mathematics, Physics and Chemistry. The questions are based on Class 11 and Class 12 syllabus. Candidates can find answers for all the questions asked in JEE Main 2020 Physics Paper (Shift 2 - 9th January) on this page.
1.An electron gun is placed inside a long solenoid of radius R on its axis. The solenoid has n turns/length and carries a current i. The electron gun shoots an electron along the radius of solenoid with speed If the electron does not hit the surface of the solenoid, maximum possible value of v is (all symbols have their standard meaning):
Solution:
Looking at the cross-section of the solenoid, Rmax of the particle’s motion has to be R/2 for it not to strike the solenoid.
Answer: (b)
2.Two identical capacitors A and B, charged to the same potential 5V are connected in two different circuit as shows below at time t=0. If the charges on capacitors A and B at time t= CR is Q_{A} and Q_{B} respectively, then (Here is the base of natural logarithm)
Solution:
For (a)
No current flows
Hence, Q_{A} = CV
For (b)
Current will flow in the circuit
I = (V/R)e^{(t/RC)}
Charge on the capacitor at any time q = Q e^{(-t/RC)}
at t =CR
q = Q e^{(-CR/RC)}
q = Q e^{-1}= Q/e
q = CV/e= Q_{B}
Answer:: (a)
3. For the four sets of three measured physical quantities as given below. Which of the following options is correct?
(i) A_{1} = 24.36, B_{1}=0.0724, C_{1}= 256.2
(ii) A_{2} = 24.44, B_{2}=16.08, C_{2}= 240.2
(iii) A_{3} = 25.2, B_{3} = 19.2812, C_{3}= 236.183
(iv) A_{4} = 25, B_{4} = 236.191, C_{4}= 19.5
Solution:
A_{1} + B_{1} +C_{1}= 280.632
A_{2} + B_{2} +C_{2}= 280.72
A_{3} + B_{3} +C_{3 }= 280.664
A_{4} + B_{4} +C_{4 }= 280.691
Hence, option (a) is correct.
4.A particle starts from the origin at t = 0 with an initial velocity of
Solution:
t= 4 sec
= 3 x 4 + (1/2) x 6 x 16
= 60 m
Answer: (a)
5. A spring mass system (mass m, spring constant k and natural length l) rest in equilibrium on a horizontal disc. The free end of the spring is fixed at the center of the disc. If the disc together with spring mass system, rotates about its axis with an angular velocity (k>>>m^{2}), the relative change in the length of the spring is best given by the option:
Solution:
Using Newton’s second law of dynamics,
k>>mω^{2}
So, (x/l_{0}) is equal to mω^{2}/k
Answer: (c)
6. A small circular loop of conducting wire has radius a and carries current i. It is placed in a uniform magnetic field B perpendicular to its plane such that when rotated slightly about its diameter and released, its starts performing simple harmonic motion of time period T. If the mass of the loop is m then
Solution:
Considering the torque situation on the loop,
The above equation is analogous to
Answer: (b)
7. A small spherical droplet of density d is floating exactly half immersed in a liquid of density ρ and surface tension T. The radius of droplet is (take note that the surface tension applied an upward force on droplet)
Solution:
In equilibrium, net external force acting on the sphere is zero.
Mg = F_{T}+B
Answer: (d)
8. A wire of length L and mass 6 x 10^{-3} kg/m per unit length is put under tension of 540N. Two consecutive frequencies that it resonates at are: 420 Hz and 490 Hz . Then L in meter is
Solution:
Key Idea: The difference of two consecutive resonant frequencies is the fundamental resonant frequency. Fundamental frequency = 490 – 420 =70 Hz
l≈2.1 m
Answer: : (b)
9. A plane electromagnetic wave is propagating along the direction
Solution:
EM wave is in direction
Electric field is in direction
Direction of propagation of EM wave is given by
Answer: (a)
10. Two gases-Argon (atomic radius 0.07 nm atomic weight 40) and Xenon (atomic radius 0.1 nm atomic weight 140) have the same number density and are at the same temperature. The ratio of their respective mean free time is closest to
Solution:
= 1.09
Answer: Closest answer is c (1.83)
11. Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1: 4, the ratio of their diameters is:
Solution:
Therefore, D_{1}:D_{2} = √2:1
Answer: (a)
12: Planets A has a mass M and radius R. Planet B has the mass and half the radius of planet A. If the escape velocities from the planets A and B are v_{A} and v_{B} respectively, then surfaces is
Solution:
We know that the escape velocity is given by
We are given that (V_{1}/V_{2}) = n/4
⇒ (n/4) = 1
⇒ n =4
Answer: (c)
13. A rod of length L has non-uniform linear mass density given by
Solution:
Here we take a small element along the length as dx at a distance x from the left end as shown
Answer: (b)
14. A particle of mass m is projected with a speed u from the ground at angle is θ = π/3 w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity ̂
Solution:
The only external force acting on the colliding system during the collision is the gravitational force. Since gravitational force is non- impulsive, the linear momentum of the system is conserved just before and just after the collision.
p_{i} = p_{f}
mu+mucosθ =2mv
So the horizontal range after the collision = vt
Answer: (a)
15. A uniformly thick wheel with moment of inertia I and radius R is free to rotate about its center of mass (see fig). A massless string is wrapped over its rim and two blocks of massless string is wrapped over its rim and two blocks of masses m_{1} and m_{2} (m_{1}>m_{2} ) are attached to the ends of string. The system is released from rest. The angular speed of the wheel when m_{1} descend by a distance h is:
Solution:
Assume initial potential energy of the blocks to be zero. Initial kinetic energy is also zero since the blocks are at rest.
When block m_{1} falls by h, m_{2} goes up by h (because of length constraint)
Final P.E = m_{2}gh – m_{1}gh
Let the final speed of the blocks be and angular velocity of the pulley be
Final K.E =
Total energy is conserved. Hence,
Solution: (a)
16. The energy required to ionise a hydrogen like ion in its ground state is 9 Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground stare?
Solution:
n_{1}=1
n_{2}= 3
For an H-like atom, ionization energy is (R)Z^{2}.
This gives Z=3
Wavelength
Answer: (b)
17. There is a small source of light at some depth below the surface of water (refractive index 4/3) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly): [Use the fact that surface area of a spherical cap of height h and radius of curvature r is 2πrh]
Solution:
The portion of light escaping into the air from the liquid will form a cone. As long as the angle of incidence on the liquid – air interface is less than the critical angle, i.e.i< θ_{c} , the light rays will undergo refraction and emerge into the air.
For i> θ_{c} , the light rays will suffer TIR. So, these rays will not emerge into the air. The portion of light rays emerging into the air from the liquid will form a cone of half angle = θ_{c}
sin θ_{c }= (1/μ_{Liq}) =3/4
cos θ_{c }=√7/4
Solid angle contained in this cone is
Percentage of light that escapes from liquid =
Putting values we get
Percentage = ((4-√7)/8) x 100% = 17%
Answer: (a)
18. An electron of mass m and magnitude of charge |e| initially at rest gets accelerated by a constant electric field E. The of charge of de-Broglie wavelength of this electron at time t ignoring relativistic effects is
Solution:
Answer: (c)
19. In LC circuit the inductance L = 40mH and C = 100 μF. If a voltage V(t) = 10sin(314t) is applied to the circuit, the current in the circuit is given as
Solution:
R = 0
= X_{C} - X_{L}
= (1/ωC) – ωL
= [(1/314 x 100 x 10^{-6})] – (314 x 40 x 10^{-3})
= 31.84 – 12.56 = 19.28 ohm
For X_{C }>X_{L}, current leads voltage by π/2
= 0.52cos(314t)
Answer: (b)
20. The current (i) in the network is
Solution:
Since the diodes are reverse biased, they will not conduct. Hence, the circuit will look like
R_{eff} = 5+10+5+10 = 30 ohm
I = 9/30 = 0.3A
Answer: (b)
21. Starting at temperature 300 K, one mole of an ideal diatomic gas (ϒ = 1.4) is first compressed adiabatically from volume to V_{1} to V_{2} = V_{1}/16. It is then allowed to expand isobarically to volume 2V_{2} . If all the processes are the quasi-static then the final temperature of the gas (^{0}K) is (to the nearest integer)
Solution:
300(V_{1}) ^{(1.4 -1)} = T_{B}(V_{1}/16)^{2/5}
T_{B }= 300 x 2^{(8/5)}
Now for BC process
(V_{B}/V_{C}) = (V_{C}/T_{C})
T_{C}= 1818 K
Answer: (1818 K)
22. An electric field
Solution:
Electric flux through a surface is
For surface ABCD
So, at all the points of this surface,
Because,
For surface BCEF
If x = 3
Answer: -48 Nm^{2}/C
23. In a Young’s double slit experiment 15 fringes are observed on a small portion of the screen when light of wavelength 500nm is used. 10 fringes are observed on the same section of the screen when another light source of wavelength λ is used. Then the value of λ is (nm)
Solution:
If the length of the segment is y,
Then y = nβ
n= no.of fringes
β = frindge width
15 x 500 x (D/d) = 10 x λ_{2} x (D/d)
λ_{2 }= 15 x 50 nm
= 750 nm
Answer: (750 nm)
24. In a meter bridge experiment S is a standard resistance. R is a resistance wire. It is found that balancing length is l = 25 cm. If R is replaced by a wire of half length and half diameter that of R of same material, then the balancing l (in cm) will now be
Solution:
(X/R) = (75/25) = 3
Then
l= 40.00 cm
Answer: (40)
25. The circuit shown below is working as a 8V dc regulated voltage source. When 12V is used as input, the power dissipated (in mW) in each diode id; (considering both zener diode are identical).
Solution:
I=[(12-8)/(200+200)]A = 4/400 = 10^{-2} A
Power loss in each diode = 4(10^{-2}) W = 40 mW
Answer: 40 mW