Practice Questions

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 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. An object is located at 2 km beneath the surface of the water. If the fractional compression ΔVV is 1. 36% , the ratio of hydraulic stress to the corresponding hydraulic strain will be ______[Given: density of water is 1000 kg m−3 and g = 9. 8 m s−2. (1) 1. 96 × 107 N m−2 (2) 1. 44 × 107 N m−2 (3) 2. 26 × 109 N m−2 (4) 1. 44 × 109 N m−2

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. 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. A light cylindrical vessel is kept on a horizontal surface. Area of the base is A. A hole of cross-sectional area a is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is (1) A (2) None of these 2a (3) 2a (4) a A A

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. 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. 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 P −V diagram of a diatomic ideal gas system going under cyclic process as shown in figure. The work done during an adiabatic process CD is (use γ = 1. 4) : JEE Main 2021 (18 Mar Shift 1) JEE Main Previous Year Paper (1) –500 J (2) –400 J (3) 400 J (4) 200 J

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. 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. 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. 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

Q6. In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius 2. 0 × 10−5 m and density 1. 2 × 103 kg m−3 ? Take viscosity of liquid = 1. 8 × 10−5 N s m−2. (Neglect buoyancy due to air). (1) 5. 8 × 10−10 N (2) 3. 9 × 10−10 N (3) 1. 8 × 10−10 N (4) 3. 8 × 10−11 N

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. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R . Assertion A : The escape velocities of planet A and B are same. But A and B are of unequal mass. Reason R: The product of their mass and radius must be same. M1R1 = M2R2 In the light of the above statements, choose the most appropriate answer from the options given below : (1) Both A and R are correct and R is the correct (2) Both A and R are correct but R is NOT the explanation of A correct explanation of A (3) A is not correct but R is correct (4) A is correct but R is not correct

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. 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. 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 %

Q7. A cord is wound round the circumference of wheel of radius r, The axis of the wheel is horizontal and the moment of inertia about it is I . A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance h, the square of angular velocity of wheel will be (1) 2mgh (2) 2mgh I+mr2 I+2mr2 (3) 2gh (4) I+mr22gh

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. A uniform heavy rod of weight 10 kg m s−2, cross-sectional area 100 cm2 and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 × 1011 N m−2. Neglecting the lateral contraction, JEE Main 2021 (31 Aug Shift 1) JEE Main Previous Year Paper find the elongation of rod due to its own weight: (1) 5 × 10−10 m (2) 4 × 10−8 m (3) 5 × 10−8 m (4) 2 × 10−9 m

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. A satellite is launched into a circular orbit of radius R around earth, while a second satellite is launched into a circular orbit of radius 1. 02 R. The percentage difference in the time periods of the two satellites is: (1) 1. 5 (2) 2. 0 (3) 0. 7 (4) 3. 0