Practice Questions

Q4. A player kicks a football with an initial speed of 25 m s−1 at an angle of 45° from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion? (Take g = 10 m s−2 ) (1) hmax = 15. 625 m, T = 1. 77 s (2) hmax = 3. 54 m, T = 0. 125 s (3) hmax = 10 m, T = 2. 5 s (4) hmax = 15. 625 m, T = 3. 54 s

Q4. List- I List- II (a) MI of the rod (length L, Mass M, about an axis ⊥ to the rod passing (i) through the midpoint) 8ML2 3 (b) MI of the rod (length L, Mass 2M, about an axis ⊥ to the rod ML2 (ii) 3 passing through one of its end) (c) MI of the rod (length 2L, Mass M, about an axis ⊥ to the rod (iii) passing through its midpoint) ML2 12 (d) MI of the rod (Length 2L, Mass 2M, about an axis ⊥ to the rod (iv) passing through one of its end) 2ML2 3 Choose the correct answer from the options given below: JEE Main 2021 (27 Jul Shift 1) JEE Main Previous Year Paper (1) (a) −(ii), (b) −(iii), (c) −(i), (d) −(iv) (2) (a) −(ii), (b) −(i), (c) − (iii), (d) −(iv) (3) (a) −(iii), (b) −(iv), (c) − (ii), (d) −(i) (4) (a) − (iii), (b) −(iv), (c) −(i), (d) −(ii)

Q4. The maximum and minimum distances of a comet from the Sun are 1. 6 × 1012 m and 8. 0 × 1010 m respectively. If the speed of the comet at the nearest point is 6 × 104 m s−1 , the speed at the farthest point is (1) 1. 5 × 103 m s−1 (2) 6. 6 × 103 m s−1 (3) 3. 0 × 103 m s−1 (4) 4. 5 × 103 m s−1

Q4. Consider two satellites 𝑆1 and 𝑆2 with periods of revolution 1hr and 8hr respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite 𝑆1 to the angular velocity of satellite 𝑆2 is: (1) 8: 1 (2) 2: 1 (3) 1: 4 (4) 1: 8

Q5. The time period of a satellite in a circular orbit of the radius R is T. The period of another satellite in a circular orbit of the radius 9R is: (1) 9T (2) 27T (3) 12T (4) 3T

Q5. The instantaneous velocity of a particle moving in a straight line is given as v = αt + βt2 , where α and β are constants. The distance travelled by the particle between 1 s and 2 s is: (1) 3α + 7β (2) 32 α + 73 β (3) α 2 + β3 (4) 32 α + 72 β Q6. → A force F = + N acts on a body of mass 5 kg. If the body starts from rest, its position vector →rat (40ˆi 10ˆj) time t = 10 s will be + + m (1) (100ˆi 400ˆj) m (2) (100ˆi 100ˆj) + + m (3) (400ˆi 100ˆj) m (4) (400ˆi 400ˆj)

Q5. If the kinetic energy of a moving body becomes four times its initial kinetic energy, then the percentage change in its momentum will be: (1) 100% (2) 200% (3) 300% (4) 400%

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. 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

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. What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature T ? ( kB is Boltzmann constant) (1) 2 1 kBT (2) 32 kBT (3) 3 kBT (4) kBT 2

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

Q7. The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from 0 °C to 50 °C when no work is done is (R is the universal gas constant) (1) 250R (2) 750R (3) 175R (4) 500R

Q7. The R.M.S. speeds of the molecules of Hydrogen, Oxygen, and Carbon dioxide at the same temperature are vH, vO and vC respectively, then: (1) vC > vO > vH (2) vH = vO > vC (3) vH > vO > vC (4) vH = vO = vC

Q7. The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is L. The magnitude of the areal velocity of the planet is : JEE Main 2021 (18 Mar Shift 2) JEE Main Previous Year Paper (1) 4L (2) L M M (3) 2L (4) L M 2M

Q8. Each side of a box made of metal sheet in cubic shape is 𝑎 at room temperature 𝑇, the coefficient of linear expansion of the metal sheet is 𝛼. The metal sheet is heated uniformly, by a small temperature 𝛥𝑇, so that its new temperature is 𝑇+ 𝛥𝑇. Calculate the increase in the volume of the metal box. (1) 4𝑎3𝛼𝛥𝑇 (2) 3𝑎3𝛼𝛥𝑇 (3) 4𝜋𝑎3𝛼𝛥𝑇 (4) 43𝜋𝑎3𝛼𝛥𝑇

Q8. The volume V of an enclosure contains a mixture of three gases, 16 g of oxygen, 28 g of nitrogen and 44 g of carbon dioxide at absolute temperature T . Consider R as universal gas constant. The pressure of the mixture of gases is : (1) 88RT (2) 3RT V V (3) 5 RT (4) 4RT 2 V V

Q8. T0 is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to 161 times of its initial value, the modified time period is (1) T0 (2) 8πT0 (3) 4T0 (4) 14 T0

Q9. Consider a mixture of gas molecule of types A, B and C having masses mA < mB < mC. The ratio of their root mean square speeds at normal temperature and pressure is: (1) vA = vB = vC = 0 (2) 1 > 1 > 1 vA vB vC (3) vA = vB ≠vC (4) 1 < 1 < 1 vA vB vC

Q9. If the time period of a two meter long simple pendulum is 2 s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is: (1) 2π2 m s−2 (2) 16 m s−2 (3) π2 m s−2 (4) 9. 8 m s−2

Q9. Match List I with List II . List I List II (a) Isothermal (i) Pressure constant (b) Isochoric (ii) Temperature constant (c) Adiabatic (iii) Volume constant (d) Isobaric (iv) Heat content is constant Choose the correct answer from the options given below: (1) ( a ) →( ii ) , ( b ) →( iii ) , ( c ) →( iv ) , ( d ) →( i ) (2) ( a ) →( iii ) , ( b ) →( ii ) , ( c ) →( i ) , ( d ) →( iv ) (3) ( a ) →( i ) , ( b ) →( iii ) , ( c ) →( ii ) , ( d ) →( iv ) (4) ( a ) →( ii ) , ( b ) →( iv ) , ( c ) →( iii ) , ( d ) →( i ) Q10.𝑛 mole of a perfect gas undergoes a cyclic process 𝐴𝐵𝐶𝐴 (see figure) consisting of the following processes. 𝐴→𝐵: Isothermal expansion at temperature 𝑇 so that the volume is doubled from 𝑉1 to 𝑉2 = 2𝑉1 and pressure changes from 𝑃1 to 𝑃2 𝐵→𝐶: Isobaric compression at pressure 𝑃2 to initial volume 𝑉1 . 𝐶→𝐴: Isochoric change leading to change of pressure from 𝑃2 to 𝑃1 Total work done in the complete cycle 𝐴𝐵𝐶𝐴 is: JEE Main 2021 (24 Feb Shift 1) JEE Main Previous Year Paper 1 (1) 𝑛𝑅𝑇ln2 - (2) 𝑛𝑅𝑇ln2 2 (3) 𝑛𝑅𝑇ln2 + 1 (4) 0 2

Q9. If the R.M.S. speed of oxygen molecules at 0°C is 160 m s−1 . Find the R.M.S. speed of hydrogen molecules at 0°C . (1) 40 m s−1 (2) 80 m s−1 (3) 640 m s−1 (4) 332 m s−1

Q9. Time period of a simple pendulum is T inside a lift when the lift is stationary. If the lift moves upwards with an acceleration g , the time period of pendulum will be : 2 (1) √3T (2) T √3 (3) (4) T T √32 √23

Q10.The temperature θ at the junction of two insulating sheets, having thermal resistances R1 and R2 as well as top and bottom temperatures θ1 and θ2 (as shown in figure) is given by : (1) θ1R2−θ2R1 (2) θ2R2−θ1R1 R2−R1 R2−R1 (3) θ1R2+θ2R1 (4) θ1R1+θ2R2 R1+R2 R1+R2

Q10.A particle starts executing simple harmonic motion (SHM) of amplitude a and total energy E. At any instant, its kinetic energy is 3E , then its displacement y is given by: 4 (1) y = a (2) y = a √2 (3) y = a√32 (4) y = a2