Practice Questions

Q50.The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the disc and rotating in similar way, is n times higher than the moment of inertia of the given ring. Here, $\mathrm{n}=_________ Consider all the bodies have equal masses.

Q50.A particle is projected at an angle of 30∘ from horizontal at a speed of 60 m/s. The height traversed by the particle in the first second is h0 and height traversed in the last second, before it reaches the maximum height, is h1 . The ratio h0 : h1 is _________ [Take, g = 10 m/s2 ]

Q50.The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of 7 × 106 Pa, would be ____ mm3 . (Given bulk modulus of copper = 1.4 × 1011 N m−2 )

Q50.At steady state the charge on the capacitor, as shown in the circuit below, is μC.

Q2. Young's modulus is determined by the equation given by Y = 49000 ml cm2dyn where M is the mass and l is the extension of wire used in the experiment. Now error in Young modules (Y ) is estimated by taking data from M −l plot in graph paper. The smallest scale divisions are 5 g and 0.02 cm along load axis and extension axis respectively. If the value of M and l are 500 g and 2 cm respectively then percentage error of Y is : (1) 0.5% (2) 2% (3) 0.02% (4) 0.2%

Q3. A clock has 75 cm, 60 cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel x distance more than the tip of minute hand. The value of x in meter is nearly (Take π = 3.14 ) : (1) 140.5 (2) 118.9 (3) 139.4 (4) 220.0

Q6. A player caught a cricket ball of mass 150 g moving at a speed of 20 m/s. If the catching process is completed in 0.1 s, the magnitude of force exerted by the ball on the hand of the player is: (1) 3 N (2) 300 N (3) 150 N (4) 30 N

Q10.A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature (27∘C). The ratio of specific heat of gases at constant volume respectively is: (1) 7 (2) 3 5 5 (3) 5 (4) 3 3 2

Q12.In the given circuit, the terminal potential difference of the cell is : (1) 2 V (2) 3 V (3) 4 V (4) 1.5 V

Q15.Critical angle of incidence for a pair of optical media is 45∘ . The refractive indices of first and second media are in the ratio: (1) 1 : √2 (2) √2 : 1 (3) 2 : 1 (4) 1 : 2

Q16.A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is: (Assume h=6.63 ×10−34 J s, me = 9.0 × 10−31 kg and mp = 1836 times me ) (1) 1 : √1836 (2) 1 : 18361 (3) 1 : 1 (4) 1: 1836 √1836

Q17.Average force exerted on a non-reflecting surface at normal incidence is 2.4 × 10−4 N. If 360 W/cm2 is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is: (1) 0.2 m2 (2) 20 m2 (3) 0.1 m2 (4) 0.02 m2

Q18.Binding energy of a certain nucleus is 18 × 108 J. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus: (1) 10μg (2) 20μg (3) 0.2μg (4) 2μg

Q20.The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to 1 mm . The main scale reading is 2 cm and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 g, the density of the sphere is: (1) 2.0 g/cm3 (2) 1.7 g/cm3 (3) 2.2 g/cm3 (4) 2.5 g/cm3 JEE Main 2024 (08 Apr Shift 1) JEE Main Previous Year Paper −−−

Q20.The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is 𝑁%. The value of 𝑁 is: (1) 4 (2) 8 (3) 6 (4) 5

Q20.While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is 1 mm and circular scale reading is equal to 42 divisions. Pitch of screw gauge is 1 mm and it has 100 divisions on circular scale. The diameter of the wire is x mm . The value of x is : 50 (1) 21 (2) 142 (3) 71 (4) 42

Q21.Three vectors OP,→ OQ→ and OR→ each of magnitude A are acting as shown in figure. The resultant of the three vectors is A√x. The value of x is ________ .

Q21.The displacement and the increase in the velocity of a moving particle in the time interval of t to (t + 1) s are 125 m and 50 m s−1 , respectively. The distance travelled by the particle in (t + 2)th s is ___________ m .

Q21.A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of 100 m from the foot of the tower. A body of mass 2M thrown at a velocity 2v from the top of the tower of height 4H will touch the ground at a distance of _____ m . JEE Main 2024 (08 Apr Shift 2) JEE Main Previous Year Paper

Q21.Two identical spheres each of mass 2 kg and radius 50 cm are fixed at the ends of a light rod so that the separation between the centers is 150 cm. Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is 𝑥 kg m2, where the value of 𝑥 is 20

Q21.The resultant of two vectors →A and →B is perpendicular to →A and its magnitude is half that of →B. The angle between vectors →A and →B is ______ ∘.

Q21.A particle is moving in a circle of radius 50 cm in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at t = 0 is 4 m s−1 , the time taken to complete the first revolution will be 1 [1 −e−2π] s, where α =______. α

Q21.A body starts falling freely from height 𝐻 hits an inclined plane in its path at height ℎ. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of 𝐻 for which ℎ the body will take the maximum time to reach the ground is _____.

Q21.A vector has magnitude same as that of 𝐴= 3 ^j + 4 ^j and is parallel to 𝐵= 4 ^i + 3 ^j. The 𝑥 and 𝑦 components of this vector in first quadrant are 𝑥 and 3 respectively where x = ____.

Q21.A particle moves in a straight line so that its displacement x at any time t is given by x2 = 1 + t2 . Its acceleration at any time t is x−n where n = ___________