Practice Questions

Q20.A transmitting antenna at top of a tower has a height of 50 m, and the height of receiving antenna is, 80 m. What is the range of communication for the line of sight (LOS) mode? [use radius of the earth = 6400 km] JEE Main 2021 (26 Aug Shift 2) JEE Main Previous Year Paper (1) 80. 2 km (2) 144. 1 km (3) 57. 28 km (4) 45. 5 km

Q20.For the circuit shown below, calculate the value of Iz : JEE Main 2021 (20 Jul Shift 1) JEE Main Previous Year Paper (1) 25 mA (2) 0. 15 A (3) 0. 1 A (4) 0. 05 A

Q20.The vernier scale used for measurement has a positive zero error of 0. 2 mm. If while taking a measurement it was noted that 0 on the vernier scale lies between 8. 5 cm and 8. 6 cm. Vernier coincidence is 6, then the correct value of measurement is cm. (least count = 0. 01 cm ) (1) 8. 36 cm (2) 8. 54 cm (3) 8. 58 cm (4) 8. 56 cm

Q20.In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0. 5 mm on a complete rotation. For a particular observation the reading on the main scale is 5 mm and the 20th division of the circular scale coincides with reference line. Calculate the true reading. (1) 5. 20 mm (2) 5. 00 mm (3) 5. 15 mm (4) 5. 25 mm

Q21.A force of F = (5y 20)ˆj y = 0 m to y = 10 m is ________ J .

Q21.The coefficient of static friction between a wooden block of mass 0 . 5 kg and a vertical rough wall is 0 . 2 . The magnitude of the horizontal force that should be applied on the block to keep it adhere to the wall will be______N. 𝑔= 10 m s-2

Q1. If speed V , area A and force F are chosen as fundamental units, then the dimension of Young's modulus will be : (1) FA2 V−1 (2) FA2 V−3 (3) FA2 V−2 (4) FA−1 V0

Q1. For the four sets of three measured physical quantities as given below. Which of the following options is correct? (i) A1 = 24.36, B1 = 0.0724, C1 = 256.2 (ii) A2 = 24.44, B2 = 16.082, C2 = 240.2 (iii) A3 = 25.2, B3 = 19.2812, C3 = 236.183 (iv) A4 = 25, B4 = 236.191, C4 = 19.5 (1) A4 + B4 + C4 < A1 + B1 + C1 < A3 + B3 + C3 < A2 + B2 + C2 (2) A1 + B1 + C1 = A2 + B2 + C2 = A3 + B3 + C3 = A4 + B4 + C4 (3) A1 + B1 + C1 < A2 + B2 + C2 = A3 + B3 + C3 < A4 + B4 + C4 (4) A1 + B1 + C1 < A3 + B3 + C3 < A2 + B2 + C2 < A4 + B4 + C4

Q1. A clock has a continuously moving second's hand of 0. 1m length. The average acceleration of the tip of the hand (in units of ms−2 ]) is of the order of : (1) 10−3 (2) 10−4 (3) 10−2 (4) 10−1

Q1. where c is speed of light, G univasal gravitational constant and h is the A quantity f is given by f = √hc5G Planck’s constant. Dimension of f is that of: (1) area (2) energy (3) momentum (4) volume →

Q1. A quantity x is given by (1Fv2/WL4 ) in terms of moment of inertia I , force F , velocity v , work W and length L. The dimensional formula for x is same as that of : (1) planck's constant (2) force constant (3) energy density (4) coefficient of viscosity

Q1. Given, B is magnetic field induction, and μ0 is the magnetic permeability of vacuum. The dimension of B2 is: 2μ0 (1) MLT−2 (2) ML2T−1 (3) ML2T−2 (4) ML−1T−2

Q1. A physical quantity z depends on four observables a, b, c and d , as z = a2b2/3 . The percentage of error in the √cd3 measurement of a, b, c and d are 2%, 1. 5%, 4% and 2. 5% respectively. The percentage of error in z is : (1) 12. 25% (2) 16. 5% (3) 13. 5% (4) 14. 5%

Q1. The quantities x = 1 , y = EB and z = CRl are defined where C-capacitance, R-Resistance, ℓ−length, E- √μ0∈0 Electric field, B-magnetic field and ∈0, μ0, −free space permittivity and permeability respectively. Then: (1) x, y and z have the same dimension. (2) Only x and z have the same dimension (3) Only x and y have the same dimension (4) Only y and z have the same dimension.

Q1. The dimension of stopping potential V0 in photoelectric effect in units of Planck’s constant ‘ h ’, speed of light ‘ c ’ and Gravitational constant ‘ G ’ and ampere A is: (1) h 31 G 32 c 31 A−1 (2) h0c5G−1A−1 (3) h−23 c−13 G 34 A−1 (4) h2G 23 c 31 A−1

Q1. If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is : (1) [P2 AT−2] (2) [PA−1 T −1] (3) [PA1/2 T−1] (4) [P 1/2 AT−1]

Q1. A 60HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to : (1 HP = 746 W, g = 10 m s−2) (1) 1.7 m s−1 (2) 1.9 m s−1 (3) 1.5 m s−1 (4) 2.0 m s−1

Q1. Dimensional formula for thermal conductivity is (here K denotes the temperature): (1) MLT –2K (2) MLT –2K–2 (3) MLT –3K (4) MLT –3K–1

Q1. Moment of inertia of a cylinder of mass m, length L and radius R about an axis passing through its centre and L2 If such a cylinder is to be made for a given mass perpendicular to the axis of the cylinder is I = + M( R24 12 ). of a material, the ratio L for it to have minimum possible I is: R (1) 2 (2) 3 3 2 (3) √32 (4) √23

Q2. Three point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The centre of mass of the system is at a point: (1) 0.6 cm right and 2.0 cm above 1 kg mass. (2) 1.5 cm right and 1.2 cm above 1 kg mass. (3) 2.0 cm right and 0.9 cm above 1 kg mass. (4) 0.9 cm right and 2.0 cm above 1 kg mass.

Q2. A spring mass system (mass m, spring constant k and natural length l ) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If the disc together with spring mass system rotates about it's axis with an angular velocity ω, (k >> mω2) the relative change in the length of the spring is best given by the option: (1) mω2 (2) 2mω2 k √23 ( k ) (3) mω2 (4) mω2 k 3k

Q2. A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed ω about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is: (1) mlω2 (2) mlω2 k−ωm k−mω2 (3) mlω2 (4) mlω2 k+mω2 k+mω

Q2. Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are 0. 1 kg −m2 and 10 rad s−1 respectively while those for the second one are 0. 2 kg −m2 and 5 rad s−1 respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The kinetic energy of the combined system is : (1) 10 3 J (2) 203 J (3) 3 5 J (4) 23 J

Q2. When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees that rain drops coming at an angle 60∘ from the horizontal. On further increasing the speed of the car to (1 + β)v, this angle changes to 45∘ . The value of β is close to : (1) 0. 50 (2) 0. 41 (3) 0. 37 (4) 0. 73 B of mass m2

Q2. An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg . The mass of the elevator itself is 920 kg and it moves with a constant speed of 3 m/s . The frictional force opposing the motion is 6000 N . If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator (g = 10m/s2) must be at least: (1) 56300W (2) 62360W (3) 48000W (4) 66000W