JEE Main 2018 physics Question Paper Set 1 With Solution

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Category: IIT-JEE 2018 Physics Paper 1

Question 1:

The potential energy of a particle of mass 𝑚 at a distance 𝑟 from a fixed point 𝑂 is given by

v (r) = k r^{2} / 2,

where 𝑘 is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius 𝑅 about the point 𝑂. If 𝑣 is the speed of the particle and 𝐿 is the magnitude of its angular momentum about 𝑂, which of the following statements is (are) true?

A	$v = \sqrt{\frac{k}{2 m}} R$	B	$V = \sqrt{\frac{K}{m}} R$
C	$L = \sqrt{m k} R^{2}$	D	$L = \sqrt{\frac{m k}{2}} R^{2}$

Correct Answer : B and C

Category: IIT-JEE 2018 Physics Paper 1

Question 2:

Consider a body of mass 1.0 𝑘𝑔 at rest at the origin at time 𝑡=0. A force

\vec{F}

= (α t \hat{I} + \hat{j})

is applied on the body, where

α = 1.0 N s^{- 1} a n d β

=1.0 𝑁. The torque acting on the body about the origin at time 𝑡=

= 1, 0 s i s \vec{τ}

. Which of the following statements is (are) true?

A	$\|\vec{τ}\| = \frac{1}{3} N m$	B	$T h e t o r q u e \vec{τ} i s i n t h e d i r e c t i o n o f t h e u n i t v e c t o r + \hat{k}$
C	The Velocity of the body at t =1 s is $\vec{v} = 12 (\hat{i} + 2 \hat{j}) m s^{- 1}$	D	The magnitude of displacement of the body at 𝑡=1 𝑠 is $\frac{1}{6} m$

Correct Answer : C and A

Category: IIT-JEE 2018 Physics Paper 1

Question 3:

A uniform capillary tube of inner radius 𝑟 is dipped vertically into a beaker filled with water. The water rises to a height ℎ in the capillary tube above the water surface in the beaker. The surface tension of water is 𝜎. The angle of contact between water and the wall of the capillary tube is 𝜃. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

A	For a given material of the capillary tube, ℎ decreases with increase in 𝑟	B	For a given material of the capillary tube, ℎ is independent of 𝜎
C	If this experiment is performed in a lift going up with a constant acceleration, then ℎ decreases	D	ℎ is proportional to contact angle 𝜃

Correct Answer : A and C

Category: IIT-JEE 2018 Physics Paper 1

Question 4:

In the figure below, the switches

s_{1}

and

s_{2}

are closed simultaneously at 𝑡=0 and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current 𝐼 in the middle wire reaches its maximum magnitude 𝐼𝑚𝑎𝑥 at time 𝑡=𝜏. Which of the following statements is (are) true?

A	$I_{m a x} = \frac{v}{2 R}$	B	$I_{m a x} = \frac{v}{4 R}$
C	$τ = \frac{L}{R} I n 2$	D	$τ = \frac{2 L}{R} I n 2$

Correct Answer : D and B

Category: IIT-JEE 2018 Physics Paper 1

Question 5:

Two infinitely long straight wires lie in the 𝑥𝑦-plane along the lines 𝑥=±𝑅. The wire located at 𝑥=+𝑅 carries a constant current

I_{1}

and the wire located at 𝑥=−𝑅 carries a constant current

I_{2}

. A circular loop of radius 𝑅 is suspended with its centre at

(0, 0, \sqrt{3 R})

and in a plane parallel to the 𝑥𝑦-plane. This loop carries a constant current 𝐼 in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the +𝑗̂ direction. Which of the following statements regarding the magnetic field 𝐵⃗ is (are) true?

A	If cannot be equal to zero at the origin (0,0,0)	B	If $I_{1} > 0 a n d I_{2} < 0, \vec{B}$ can be equal to zero at the origin (0,0,0)
C	If $I_{1} < 0 a n d I_{2} > 0, \vec{B}$ can be equal to zero at the origin (0,0,0)	D	If $I_{1} = I_{2}$ then the 𝑧-component of the magnetic field at the centre of the loop is $(- \frac{μ_{o} 1}{2 R})$

Correct Answer : A,B and D

Category: IIT-JEE 2018 Physics Paper 1

Question 6:

One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where V is the volume and T is the temperature). Which of the statements below is (are) true?

A	Process I is an isochoric process	B	In process II, gas absorbs heat
C	In process IV, gas releases heat	D	Processes I and III are not isobaric

Correct Answer : B,C and D

Category: IIT-JEE 2018 Physics Paper 1

Question 7:

Two vectors

\vec{A}

and

\vec{B}

are defined as

\vec{A}

=𝑎 𝑖̂ and

\vec{B}

=𝑎 (cos𝜔𝑡𝑖̂+sin𝜔𝑡𝑗̂), where 𝑎 is a constant and 𝜔=𝜋/6 𝑟𝑎𝑑

S^{- 1}

. If |

|\vec{A} + \vec{B}|

= \sqrt{3} |\vec{A} + \vec{B}|

time 𝑡=𝜏 for the first time, the value of 𝜏, in 𝑠𝑒𝑐𝑜𝑛𝑑𝑠, is __________.

Correct Answer : 2.00

Category: IIT-JEE 2018 Physics Paper 1

Question 8:

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed 1.0 𝑚

s^{- 1}

and the man behind walks at a speed 2.0 𝑚

s^{- 1}

. A third man is standing at a height 12 𝑚 above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency 1430 𝐻𝑧. The speed of sound in air is 330 𝑚

s^{- 1}

. At the instant, when the moving men are 10 𝑚 apart, the stationary man is equidistant from them. The frequency of beats in 𝐻𝑧, heard by the stationary man at this instant, is __________.

Correct Answer : 5.00

Category: IIT-JEE 2018 Physics Paper 1

Question 9:

A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an angle 60° with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is

(2 - \sqrt{3}) / \sqrt{10} s,

, then the height of the top of the inclined plane, in 𝑚𝑒𝑡𝑟𝑒𝑠, is __________. Take

g = 10 m s^{- 2}

Correct Answer : 0.75

Category: IIT-JEE 2018 Physics Paper 1

Question 10:

A spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is 2.0 𝑁

m^{- 1}

and the mass of the block is 2.0 𝑘𝑔. Ignore the mass of the spring. Initially the spring is in an unstretched condition. Another block of mass 1.0 𝑘𝑔 moving with a speed of 2.0

m s^{- 1}

collides elastically with the first block. The collision is such that the 2.0 𝑘𝑔 block does not hit the wall. The distance, in 𝑚𝑒𝑡𝑟𝑒𝑠, between the two blocks when the spring returns to its unstretched position for the first time after the collision is _________.

Correct Answer : 2.09

Category: IIT-JEE 2018 Physics Paper 1

Question 11:

Three identical capacitors

c_{1}

c_{2}

and

c_{3}

have a capacitance of 1.0 𝜇𝐹 each and they are uncharged initially. They are connected in a circuit as shown in the figure and 𝐶1 is then filled completely with a dielectric material of relative permittivity 𝜖𝑟. The cell electromotive force (emf) 𝑉0=8 𝑉. First the switch

s_{1}

is closed while the switch

s_{2}

is kept open. When the capacitor

c_{3}

is fully charged,

s_{1}

is opened and

s_{2}

is closed simultaneously. When all the capacitors reach equilibrium, the charge on

c_{3}

is found to be 5 𝜇𝐶. The value of

ε_{r}

=____________.

Correct Answer : 1.50

Category: IIT-JEE 2018 Physics Paper 1

Question 12:

In the 𝑥𝑦-plane, the region 𝑦>0 has a uniform magnetic field

B_{1} \hat{K}

and the region 𝑦<0 has another uniform magnetic field

B_{2} \hat{K}

. A positively charged particle is projected from the origin along the positive 𝑦-axis with speed 𝑣0=𝜋 𝑚

S^{- 1}

at 𝑡=0, as shown in the figure. Neglect gravity in this problem. Let 𝑡=𝑇 be the time when the particle crosses the 𝑥-axis from below for the first time. If

B_{2}

B_{1}

, the average speed of the particle, in 𝑚

S^{- 1}

, along the 𝑥-axis in the time interval 𝑇 is __________.

Correct Answer : 2.00

Category: IIT-JEE 2018 Physics Paper 1

Question 13:

Sunlight of intensity 1.3 𝑘𝑊

m^{- 2}

is incident normally on a thin convex lens of focal length 20 𝑐𝑚. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, in 𝑘𝑊

m^{- 2}

, at a distance 22 𝑐𝑚 from the lens on the other side is __________.

Correct Answer : 130.00

Category: IIT-JEE 2018 Physics Paper 1

Question 14:

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures

T_{1}

=300 𝐾 and

T_{2}

=100 𝐾, as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are

K_{1}

and

K_{2}

respectively. If the temperature at the junction of the two cylinders in the steady state is 200 𝐾, then

K_{1} / K_{2}

=__________.

Correct Answer : 4.00

Category: IIT-JEE 2018 Physics Paper 1

Question 15:

[\in_{0}]

and

[μ_{0}]

stand for dimensions of the permittivity and permeability of free space respectively. [𝐿] and [𝑇] are dimensions of length and time respectively. All the quantities are given in SI units. The relation between [E] and [B] is

A	[E] =[B] [L][T]	B	[E]= $[B] {[L]}^{- 1} [T]$
C	$[E] = [B] [L] {[T]}^{- 1}$	D	$[E] = [B] {[L]}^{- 1} {[T]}^{- 1}$

Correct Answer : C

Category: IIT-JEE 2018 Physics Paper 1

Question 16:

If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation 𝑧= 𝑥/𝑦. If the errors in 𝑥, 𝑦 and 𝑧 are Δ𝑥,Δ𝑦 and Δ𝑧, respectively, then

z \pm Δ z = \frac{x + Δ x}{y + Δ y} = \frac{x}{y} (1 \pm \frac{Δ x}{x}) {(1 \pm \frac{Δ y}{y})}^{- 1}

The series expansion for

{(1 \pm \frac{Δ y}{y})}^{- 1}

to first power inΔ𝑦/𝑦, is 1∓(Δ𝑦/𝑦). The relative errors in independent variables are always added. So the error in 𝑧 will be

Δ z = z (\frac{Δ x}{x}) + (\frac{Δ y}{y}) .

The above derivation makes the assumption that Δ𝑥/𝑥≪1, Δ𝑦/𝑦≪1. Therefore, the higher powers of these quantities are neglected. Consider the ratio 𝑟=

\frac{(1 - a)}{(1 + a)}

to be determined by measuring a dimensionless quantity 𝑎. If the error in the measurement of 𝑎 is Δ𝑎 (Δ𝑎/𝑎≪1) , then what is the error Δ𝑟 in determining 𝑟?

A	$\frac{∆ a}{{(1 + a)}^{2}}$	B	$\frac{2 ∆ a}{{(1 + a)}^{2}}$
C	$\frac{∆ a}{(1 - a^{2})}$	D	$\frac{2 a ∆ a}{(1 - a^{2})}$

Correct Answer : B

Category: IIT-JEE 2018 Physics Paper 1

Question 17:

z \pm Δ z = \frac{x + Δ x}{y + Δ y} = \frac{x}{y} (1 \pm \frac{Δ x}{x}) {(1 \pm \frac{Δ y}{y})}^{- 1}

The series expansion for

{(1 \pm \frac{Δ y}{y})}^{- 1}

to first power inΔ𝑦/𝑦, is 1∓(Δ𝑦/𝑦). The relative errors in independent variables are always added. So the error in 𝑧 will be

Δ z = z (\frac{Δ x}{x}) + (\frac{Δ y}{y}) .

The above derivation makes the assumption that Δ𝑥/𝑥≪1, Δ𝑦/𝑦≪1. Therefore, the higher powers of these quantities are neglected. Consider the ratio 𝑟=

r = \frac{(1 - a)}{(1 + a)}

In an experiment, the initial number of radioactive nuclei is 3000. It is found that 1000±40 nuclei decayed in the first 1.0 𝑠. For |𝑥|≪1, ln(1+𝑥)=𝑥 up to first power in 𝑥. The error Δ𝜆, in the determination of the decay constant 𝜆, in 𝑠−1, is

A	0.04	B	0.03
C	0.02	D	0.01

Correct Answer : C

Category: IIT-JEE 2018 Physics Paper 1

Question 18:

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, [𝐸] and [𝐵] stand for dimensions of electric and magnetic fields respectively, while and stand for dimensions of the permittivity and permeability of free space respectively. [𝐿] and [𝑇] are dimensions of length and time respectively. All the quantities are given in SI units. The relation between

[\in_{0}]

and

[μ_{0}]

A	$[μ_{0}] = [\in_{0}] {[L]}^{2} {[T]}^{- 2}$	B	$[μ_{0}] = [\in_{0}] {[L]}^{- 2} {[T]}^{2}$
C	$[μ_{0}] = {[\in_{0}]}^{- 1} {[L]}^{2} {[T]}^{- 2}$	D	$[μ_{0}] = {[\in_{0}]}^{- 1} {[L]}^{- 2} {[T]}^{2}$

Correct Answer : D

JEE Main 2018 physics Question Paper Set 1 With Solution

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