Practice Questions

Q6. Electric field of a plane electromagnetic wave propagating through a non-magnetic medium is given by 𝐸= 20cos2 × 1010𝑡- 200𝑥 V m-1 . The dielectric constant of the medium is equal to: (Take 𝜇𝑟= 1 ) (1) 2 (2) 1 3 (3) 9 (4) 3

Q6. A planet revolving in elliptical orbit has : A. a constant velocity of revolution. B. has the least velocity when it is nearest to the sun. C. its areal velocity is directly proportional to its velocity. D. areal velocity is inversely proportional to its velocity. E. to follow a trajectory such that the areal velocity is constant. Choose the correct answer from the options given below: (1) A only (2) C only (3) E only (4) D only

Q6. When two soap bubbles of radii a and b(b > a) coalesce, the radius of curvature of common surface is: (1) ab (2) a+b b−a ab (3) b−a (4) ab ab a+b

Q6. A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic energy. The body is: (1) solid sphere (2) solid cylinder (3) hollow cylinder (4) ring

Q6. The height of victoria's falls is 63 m. What is the difference in the temperature of water at the top and at the bottom of the fall? [Given 1 cal = 4. 2 J and specific heat of water = 1 cal g−1 ∘C−1] (1) 14. 76 °C (2) 1. 476 °C (3) 0. 147 °C (4) 0. 014 °C

Q6. The value of tension in a long thin metal wire has been changed from T1 to T2 . The lengths of the metal wire at two different values of tension T1 and T2 are ℓ1 and ℓ2 , respectively. The actual length of the metal wire is: (1) T1ℓ2−T2ℓ1 (2) T1ℓ1−T2ℓ2 T 1−T2 T 1−T2 (3) ℓ1+ℓ2 (4) √T1 T 2ℓ1ℓ2 2

Q6. The solid cylinder of length 80 cm and mass M has a radius of 20 cm. Calculate the density of the material used if the moment of inertia of the cylinder about an axis CD parallel to AB as shown in figure is 2. 7 kg m2 . JEE Main 2021 (26 Aug Shift 2) JEE Main Previous Year Paper (1) 1. 49 × 102 kg m−3 (2) 7. 5 × 101 kg m−3 (3) 14. 9 kg m−3 (4) 7. 5 × 102 kg m−3

Q6. Two masses A and B, each of mass M are fixed together by a massless spring, A force acts on the mass B as shown in figure. If the mass A starts moving away from mass B with acceleration a, then the acceleration of mass B will be : (1) MF (2) F+Ma F+Ma M (3) Ma−F (4) F−Ma M M JEE Main 2021 (26 Feb Shift 2) JEE Main Previous Year Paper

Q6. Two wires of same length and radius are joined end to end and loaded. The Young's moduli of the materials of the two wires are 𝑌1 and 𝑌2. The combination behaves as a single wire then its Young's modulus is: (1) 𝑌= 2𝑌1𝑌2 (2) 𝑌= 2𝑌1𝑌2 3𝑌1 + 𝑌2 𝑌1 + 𝑌2 𝑌1𝑌2 𝑌1𝑌2 (3) 𝑌= (4) 𝑌= 2𝑌1 + 𝑌2 𝑌1 + 𝑌2

Q6. A solid cylinder of mass m is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is: [The coefficient of static friction, μs , is 0. 4 ] (1) 7 mg (2) 5mg 2 (3) mg (4) 0 5 →

Q6. Two stars of masses 𝑚 and 2𝑚 at a distance 𝑑 rotate about their common centre of mass in free space. The period of revolution is 2𝜋√ (1) 2𝜋√𝑑3 (2) 3𝐺𝑚 𝑑3 3𝐺𝑚 (3) 1 3𝐺𝑚 (4) 1 2𝜋√ 𝑑3 2𝜋√𝑑33𝐺𝑚

Q6. Two identical particles of mass 1 kg each go round a circle of radius R , under the action of their mutual gravitational attraction. The angular speed of each particle is: (1) √ 2R3G (2) 21 √GR3 (3) 1 (4) 2R √1G √2GR3

Q6. The pressure acting on a submarine is 3 × 105 Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be: (Assume that atmospheric pressure is 1 × 105 Pa density of water is 103 kg m−3, g = 10 ms−2 ) (1) 200 3 % (2) 2005 % (3) 200 5 % (4) 2003 %

Q6. An electric appliance supplies 6000 J min−1 , heat to the system. If the system delivers a power of 90 W. How long it would take to increase the internal energy by 2. 5 × 103 J? (1) 2. 5 × 101 s (2) 2. 5 × 102 s (3) 2. 4 × 103 s (4) 4. 1 × 101 s

Q6. If 𝑅𝐸 be the radius of Earth, then the ratio between the acceleration due to gravity at a depth 𝑟 below and a height 𝑟 above the earth surface is: (Given : 𝑟< 𝑅𝐸) (1) 𝑟 𝑟2 𝑟3 (2) 𝑟 𝑟2 𝑟3 2 - 2 + 1 + 𝑅𝐸- 𝑅𝐸 𝑅𝐸3 1 + 𝑅𝐸+ 𝑅𝐸 𝑅𝐸3 (3) 1 - 𝑟 𝑟22 - 𝑟33 (4) 1 + 𝑟 𝑟22 + 𝑟33 𝑅𝐸- 𝑅𝐸 𝑅𝐸 𝑅𝐸- 𝑅𝐸 𝑅𝐸

Q6. Two identical springs of spring constant 2k are attached to a block of mass m and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is : (1) π√mk (2) 2π√m2k (3) π√m2k (4) 2π√mk

Q6. The masses and radii of the earth and moon are (M1, R1) and (M2, R2) respectively. Their centres are at a distance r apart. Find the minimum escape velocity for a particle of mass m to be projected from the middle of these two masses : (1) (2) 1 ve = √4G(M1+M2)r ve = 2 √2G(M1+M2)r (3) 1 (4) √2G(M1+M2) ve = r ve = 2 √4G(M1+M2)r

Q7. Four particles each of mass 𝑀, move along a circle of radius 𝑅 under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is : (1) 1 𝐺𝑀 + 1 (2) 1 𝐺𝑀 2√ 𝑅2√2 2√ 𝑅( 2√2 + 1 ) (3) 1 𝐺𝑀 - 1 (4) 𝐺𝑀 2√ 𝑅2√2 √ 𝑅

Q7. An ideal gas is expanding such that PT 3 = constant. The coefficient of volume expansion of the gas is: (1) T2 (2) T3 (3) T1 (4) T4

Q7. A body takes 4 min to cool from 61°C to 59°C. If the temperature of the surroundings is 30°C, the time taken by the body to cool from 51°C to 49°C is: (1) 4 min. (2) 3 min. (3) 8 min. (4) 6 min.

Q7. Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If √8R is the distance between the centres of a ring (of mass m ) and a sphere (mass M ) where both have equal radius R JEE Main 2021 (26 Feb Shift 1) JEE Main Previous Year Paper (1) 2√2 GMm (2) √8 GmM 3 R2 9 R 1 GMm (3) R2 (4) √827 GmMR2 3√8

Q7. Two identical metal wires of thermal conductivities K1 and K2 respectively are connected in series. The effective thermal conductivity of the combination is: (1) 2 K1 K2 (2) K1+K2 K1+K2 2 K1 K2 (3) K1+K2 (4) K1 K2 K1 K2 K1+K2

Q7. The point A moves with a uniform speed along the circumference of a circle of radius 0. 36 m and covers 30° in 0. 1 s. The perpendicular projection P from A on the diameter MN represents the simple harmonic motion of P . The restoration force per unit mass when P touches M will be : (1) 0. 49 N (2) 9. 87 N (3) 50 N (4) 100 N

Q7. Two discs have moments of intertia I1 and I2 about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, ω1 and ω2 respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by: (1) I1I2 (ω1 −ω2)2 (2) (ω1−ω2)2 (I1+I2) 2(I1+I2) (3) I1I2 (ω1 −ω2)2 (4) (I1−I2)2ω1ω2 2(I1+I2) 2(I1+I2)

Q7. What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T? (1) 2 3 kBT (2) kBT (3) 2 3 kBT (4) 21 kBT