Practice Questions

Q3. The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of, 20 m s−2 . The gases come out at a relative speed of 500 m s−1 , with respect to the rocket: [Use g = 10 m s−2] (1) 10 kg s−1 (2) 60 kg s−1 (3) 500 kg s−1 (4) 6. 0 × 102 kg s−1

Q3. Which of the following is not a dimensionless quantity? (1) Power factor (2) Quality factor (3) Permeability of free space (μ0) (4) Relative magnetic permeability (μr)

Q3. If velocity 𝑉 time 𝑇 and force 𝐹 are chosen as the base quantities, the dimensions of the mass will be : (1) 𝐹𝑉𝑇-1 (2) 𝐹𝑇-1𝑉-1 (3) 𝐹𝑇2 𝑉 (4) 𝐹𝑇𝑉-1

Q3. The motion of a mass on a spring, with spring constant K is as shown in figure. The equation of motion is given by, x(t) = A sin ωt+B cos ωt with ω = . √Km Suppose that at time t = 0, the position of mass is x(0) and velocity v(0), then its displacement can also be represented as x(t) = C cos(ωt −ϕ), where C and ϕ are (1) v(0) (2) x(0)ω + ϕ = C = √2v(0)2ω2 ω2 x(0)2, tan−1( 2v(0) ) + x(0)2, ϕ = tan−1( x(0)ω ) C = √2v(0)2 (3) x(0)ω (4) v(0) C = + ϕ = C = + ϕ = ω2 x(0)2, tan−1( x(0)ω ) ω2 x(0)2, tan−1( v(0) ) √v(0)2 √v(0)2

Q3. Moment of inertia M . I . of four bodies, having same mass and radius, are reported as; 𝐼1 = M . I . of thin circular ring about its diameter, 𝐼2 = M . I . of circular disc about an axis perpendicular to disc and going through the centre, 𝐼3 = M . I . of solid cylinder about its axis and 𝐼4 = M . I . of solid sphere about its diameter. Then: 5 (1) 𝐼1 + 𝐼2 = 𝐼3 + 2𝐼4. (2) 𝐼1 + 𝐼3 < 𝐼2 + 𝐼4 (3) 𝐼1 = 𝐼2 = 𝐼3 > 𝐼4 (4) 𝐼1 = 𝐼2 = 𝐼3 < 𝐼4

Q3. A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R3 . Its time period of revolution will be given by : (1) T ∝R 43 (2) T ∝R 25 (3) T ∝R 32 (4) T ∝R2

Q3. A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle θ as shown in figure. The coefficient of kinetic friction is μK . Then, the block's acceleration a is given by : ( g is acceleration due to gravity) (1) −Fm cos θ −μK(g −Fm sin θ) (2) mF cos θ −μK(g −Fm sin θ) (3) m F cos θ −μK(g + mF sin θ) (4) mF cos θ + μK(g −Fm sin θ)

Q4. A body of mass M moving at speed V0 collides elastically with a mass m at rest. After the collision, the two masses move at angles θ1 and θ2 with respect to the initial direction of motion of the body of mass M.. The largest possible value of the ratio M m , for which the angles θ1 and θ2 will be equal, is : (1) 3 (2) 4 (3) 2 (4) 1

Q4. A block of mass 𝑚 slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is: Given 𝑚= 8 kg, 𝑀= 16 kg Assume all the surfaces shown in the figure to be frictionless. 3 4 (1) g (2) g 5 3 6 2 (3) g (4) 5 3g

Q4. A sphere of mass 2 kg and radius 0. 5 m is rolling with an initial speed of 1 m s−1 goes up an inclined plane which makes an angle of 30° with the horizontal plane, without slipping. How low will the sphere take to return to the starting point A ? (1) 0. 60 s (2) 0. 52 s (3) 0. 56 s (4) 0. 80 s

Q4. The trajectory of a projectile in a vertical plane is y = αx −βx2, where α and β are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection θ and the maximum height attained H are respectively given by (1) tan−1 α, 4α2β (2) tan−1( αβ ), α2β (3) tan−1 β, α22β (4) tan−1 α, α24β

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. A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that r = L . The speed of particle will be : √2 (1) √rg (2) √2rg (3) √rg2 (4) 2√rg

Q4. A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time t1. If he remains stationary on a moving escalator then the escalator takes him up in time t2. The time taken by him to walk up on the moving escalator will be: (1) t1t2 (2) t1+t2 t2−t1 2 (3) t1t2 (4) t2 −t1 t2+t1

Q4. A huge circular arc of length 4. 4 ly subtends an angle 4s at the centre of the circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second? Given : 1 ly = 9. 46 × 1015 m 1 AU = 1. 5 × 1011 m (1) 3. 5 × 106 s (2) 4. 5 × 1010 s (3) 4. 1 × 108 s (4) 7. 2 × 108

Q4. A balloon was moving upwards with a uniform velocity of 10 m s−1 . An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon from the ground when object strikes the ground was around: (takes the value of g as 10 m s−2 ) (1) 300 m (2) 200 m (3) 125 m (4) 250 m

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. A thin circular ring of mass M and radius r is rotating about its axis with an angular speed ω. Two particles having mass m each are now attached at diametrically opposite points. The angular speed of the ring will become: (1) ω M (2) ω M+2M m M+m M m M−2 (3) ω (4) ω m m M+2 M+2

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

Q4. A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the work done by the porter in lowering the suitcase. (take g = 9. 8 ms−2 ) (1) −62720. 0 J (2) −627. 2 J (3) +627. 2 J (4) 784. 0 J

Q4. A triangular plate is shown. A force F = 4ˆi −3ˆj is applied at point P. The torque at point P with respect to point O and Q are: (1) −15 −20√3, 15 −20√3 (2) 15 + 20√3, 15 −20√3 (3) 15 −20√3, 15 + 20√3 (4) −15 + 20√3, 15 + 20√3

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. Thermodynamic process is shown below on a P −V diagram for one mole of an ideal gas. If V2 = 2V1 , then the ratio of temperature T2 is : T1 (1) √2 (2) 1 √2 (3) 1 (4) 2 2

Q4. Inside a uniform spherical shell : (a) The gravitational field is zero. (b) The gravitational potential is zero. (c) The gravitational field is the same everywhere. (d) The gravitation potential is the same everywhere. (e) All the above. Choose the most appropriate answer from the options given below: (1) (a), (c) and (d) only (2) (a), (b) and (c) only (3) (b), (c) and (d) only (4) (e) only

Q4. A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre with a force F1. Now a spherical cavity of radius ( R2 ) is made in the sphere (as shown in figure) and the force becomes F2 . The value of F1 : F2 is: (1) 41 : 50 (2) 50 : 41 (3) 25 : 36 (4) 36 : 25 JEE Main 2021 (25 Feb Shift 1) JEE Main Previous Year Paper