Practice Questions

Q2. A bullet of 4 g mass is fired from a gun of mass 4 kg. If the bullet moves with the muzzle speed of 50 ms1, the impulse imparted to the gun and velocity of recoil of gun are (1) 0. 4 kg m s−1, 0. 1 m s−1 (2) 0. 2 kg m s−1, 0. 05 m s−1 (3) 0. 2 kg m s−1, 0. 1 m s−1 (4) 0. 4 kg m s−1, 0. 05 m s−1

Q2. A ball is thrown up with a certain velocity so that it reaches a height h. Find the ratio of the two different times of the ball reaching h in both the directions. 3 (1) √2−1 (2) 1 √2+1 3 (3) √3−√2 (4) √3−1 √3+√2 √3+1

Q2. The angle between vector and A − is : (A) ( B) (1) tan−1( A−BB cossinθ θ ) (2) tan−1( 2√3A−BB ) √3 (3) tan−1( A−B−B2 (4) tan−1( 0.7BA ) 2 )

Q2. Match List I with List II. List-I List-II a Capacitance, C i M1 L1 T−3 A−1 b Permittivity of free space, ε0 ii M−1 L−3 T4 A2 c Permeability of free space, μ0 iii M−1 L−2 T4 A2 d Electric field, E iv M1L1T−2A−2 Choose the correct answer from the options given below (1) (a ) → (iii ), ( b ) →(ii), (c) →(iv), (d) → (i) (2) (a ) → (iii ), ( b ) → (iv ), ( c ) → (ii ), ( d ) → (i) (3) (a ) → (iv ), ( b ) → (ii ), ( c ) → (iii ), ( d ) →(4)(i)(a ) → (iv ), ( b ) → (iii ), ( c ) → (ii ), ( d ) → (i)

Q2. A butterfly is flying with a velocity 4√2 m s−1 in north-east direction. Wind is slowly blowing at 1 m s−1 from north to south. The resultant displacement of the butterfly in 3 seconds is: (1) 3 m (2) 20 m (3) 12√2 m (4) 15 m

Q2. If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density: (1) [FL−4 T2] (2) [FL−3 T3] (3) [FL−3 T2] (4) [FL−5 T2]

Q2. If two similar springs each of spring constant K1 are joined in series, the new spring constant and time period would be changed by a factor: (1) 12 , 2√2 (2) 41 , √2 (3) 14 , 2√2 (4) 21 , √2

Q2. The force is given in terms of time t and displacement x by the equation F = A cos Bx + C sin Dt The dimensional formula of AD is: B (1) [M0 L T−1] (2) [ML2 T−3] (3) [M1 L1 T−2] (4) [M2 L2 T−3]

Q2. Match List - I with List - II : List −I List −II (a) h (Planck's constant) (i) [MLT−1] (b) E (kinetic energy) (ii) [ML2 T−1] (c) V (electric potential) (iii) [ML2 T−2] (d) P (linear momentum) (iv) [ML2 I−1 T−3] Choose the correct answer from the options given below: (1) (a) →(ii), (b) →(iii), (c) →(iv), (d) →(i) (2) (a) →(i), (b) →(ii), (c) →(iv), (d) →(iii) (3) (a) →(iii), (b) →(ii), (c) →(iv), (d) →(i) (4) (a) →(iii), (b) →(iv), (c) →(ii), (d) →(i)

Q2. If E and H represents the intensity of electric field and magnetizing field respectively, then the unit of HE will be: (1) joule (2) ohm (3) newton (4) mho

Q2. A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm. If the block takes 40 s to complete one round, the normal force by the side walls of the groove is: (1) 0. 0314 N (2) 9. 859 × 10−2 N (3) 6. 28 × 10−3 N (4) 9. 859 × 10−4 N

Q2. Two identical blocks A and B each of mass m resting on the smooth horizontal floor are connected by a light spring of natural length L and spring constant K . A third block C of mass m moving with a speed v along the line joining A and B collides with A.The maximum compression in the spring is (1) v√m2K (2) √mv2K (3) √mvK (4) √m2K

Q3. Water drops are falling from a nozzle of a shower onto the floor from a height of 9. 8 m. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor. (1) 2. 94 m (2) 4. 18 m (3) 2. 45 m (4) 7. 35 m

Q3. A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies T are constants. The force acts only for −( t−TT )2] where F0 and with time according to the relation F = F0[1 the time interval 2 T . The velocity v of the particle after time 2 T is: (1) 2 F 0 T (2) F0 T M 2M (3) 4 F 0 T (4) F0 T 3M 3M

Q3. A scooter accelerates from rest for time t1 at constant rate a1 and then retards at constant rate a2 for time t2 and comes to rest. The correct value of t1 will be : t2 (1) a2 (2) a1 a1 a2 (3) a1+a2 (4) a1+a2 a1 a2

Q3. A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time t is proportional to: (1) t 32 (2) t 21 (3) t 14 (4) t 43

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 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)

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. The relation between time t and distance x for a moving body is given as t = mx2 + nx, where m and n are constants. The retardation of the motion is: (When v stands for velocity) (1) 2mv3 (2) 2mnv3 (3) 2nv3 (4) 2n2v3

Q3. Match List - I with List - II : List - I List - II a Magnetic induction i ML2 T−2 A−1 b Magnetic flux ii M0 L−1 A c Magnetic permeability iii MT−2 A−1 d Magnetization iv MLT−2 A−2 Choose the most appropriate answer from the options given below : (1) (a) −(iii), (b) −(ii), (c) −(iv), (d) −(i) (2) (a) −(iii), (b) −(i), (c) −(iv), (d) −(ii) (3) (a) −(ii), (b) −(iv), (c) −(i), (d) −(iii) (4) (a) −(ii), (b) −(i), (c) −(iv), (d) −(iii)

Q3. A helicopter is flying horizontally with a speed v at an altitude h has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped ? (1) √2ghv2+1h2 (2) √2ghv2 + h2 + h2 + h2 √2v2g (3) √2ghv2 (4) h

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. 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. The ranges and heights for two projectiles projected with the same initial velocity at angles 42° and 48° with the horizontal are 𝑅1, 𝑅2 and 𝐻1, 𝐻2 respectively. Choose the correct option: (1) 𝑅1 = 𝑅2 and 𝐻1 = 𝐻2 (2) 𝑅1 = 𝑅2 and 𝐻1 < 𝐻2 (3) 𝑅1 > 𝑅2 and 𝐻1 = 𝐻2 (4) 𝑅1 < 𝑅2 and 𝐻1 < 𝐻2 JEE Main 2021 (01 Sep Shift 2) JEE Main Previous Year Paper