Practice Questions

Q22.A series LCR circuit consists of R = 80 Ω. XL = 100 Ω , and XC = 40 Ω. The input voltage is 2500 cos(100πt) V. The amplitude of current, in the circuit, is _____ A .

Q22.A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52 . 5 N. The angular acceleration of the cylinder will be _____ rad s-2.

Q22.An inductor of inductance 2 μH is connected in series with a resistance, a variable capacitor and an AC source of frequency 7 kHz. The value of capacitance for which maximum current is drawn into the circuit is x1 F , where the value of x is ______. (Take π = 227 )

Q22.A force of -𝑃 ^𝑘 acts on the origin of the coordinate system. The torque about the point ( 2, - 3 ) is 𝑃(𝑎 ^𝑖+ 𝑏 ^𝑗) 𝑎 𝑥 , The ratio of is The value of 𝑥 is 𝑏 2.

Q22.Two concentric circular coils with radii 1 cm and 1000 cm and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be _____ ×10–8 H . (Take, π2 = 10 )

Q22.A force 𝐹= 2 + 3𝑥 ^𝑖 acts on a particle in the 𝑥 direction where 𝐹 is in Newton and 𝑥 is in meter. The work done by this force during a displacement from 𝑥 = 0 to 𝑥= 4 m is _____ J.

Q22.A thin uniform rod of length 2 m, cross sectional area 𝐴 and density 𝑑 is rotated about an axis passing through the centre and perpendicular to its length with angular velocity 𝜔. If value of 𝜔 in terms of its 𝛼𝐸 rotational kinetic energy 𝐸 is √ 𝐴𝑑, then the value of 𝛼 is ______.

Q22.An LCR series circuit of capacitance 62. 5 nF and resistance of 50 Ω, is connected to an A.C. source of frequency 2. 0 kHz . For maximum value of amplitude of current in circuit, the value of inductance is ____ mH . (Take π2 = 10)

Q22.A metallic cube of side 15 cm moving along y-axis at a uniform velocity of 2 m s−1 . In a region of uniform magnetic field of magnitude 0. 5 T directed along z- axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be mV.

Q23.Two wires each of radius 0 . 2 cm and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is ______10 – 6 m. [Young's modulus for steel = 2 × 1011 N m – 2 and 𝑔= 10 m s – 2] JEE Main 2023 (10 Apr Shift 1) JEE Main Previous Year Paper

Q23.A coil has an inductance of 2 H and resistance of 4 Ω. A 10 V is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be _____ ×10−2 J

Q23.A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is 7 × 10-3 J. The speed of the centre of mass of the sphere is ______ cm s-1.

Q23.A certain pressure '𝑃' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to 0 . 01% whereas the liquid gets compressed to 0 . 03%. The ratio of Bulk modulus of water to that of the liquid 3 is 𝑥. The value of 𝑥 is ______.

Q23.An oscillating LC circuit consists of a 75 mH inductor and a 1. 2 µF capacitor. If the maximum charge to the capacitor is 2. 7 µC. The maximum current in the circuit will be _______ mA.

Q23.The general displacement of a simple harmonic oscillator is 𝑥= 𝐴 sin 𝜔𝑡. Let 𝑇 be its time period. The 𝑇 slope of its potential energy (𝑈) – time (𝑡) curve will be maximum when 𝑡= 𝛽. The value of 𝛽 is ______.

Q23.Solid sphere 𝐴 is rotating about an axis 𝑃𝑄. If the radius of the sphere is 5 cm, then its radius of gyration about 𝑃𝑄 will be √𝑥 cm. The value of 𝑥 is _____.

Q23.Two identical solid spheres each of mass 2 kg and radii 10 cm are fixed at the ends of a light rod. The separation between the centres of the spheres is 40 cm . The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is______ × 10 – 3 kg m2 .

Q23.There is an air bubble of radius 1. 0 mm in a liquid of surface tension 0. 075 N m–1 and density 1000 kg m–3 at a depth of 10 cm below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is _______ Pa(g = 10 m s−2).

Q23.A solid sphere of mass 500 g radius 5 cm is rotated about one of its diameter with angular speed of 10 rad s-1. If the moment of inertia of the sphere about its tangent is 𝑥× 10-2 times its angular momentum about the diameter. Then the value of 𝑥 will be

Q23.Two plates A and B have thermal conductivities 84 W m-1 K-1 and 126 W m-1 K-1 respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of A and B are kept at 100∘C and 0∘C respectively, then the temperature of the surface of contact in steady state is_____ ∘C.

Q23.Figure below shows a liquid being pushed out of the tube by a piston having area of cross section 2 . 0 cm2. The area of cross section at the outlet is 10 mm2. If the piston is pushed at a speed of 4 cm s-1, the speed of outgoing fluid is _____ cm s-1

Q24.Two transparent media having refractive indices 1. 0 and 1. 5 are separated by a spherical refracting surface of radius of curvature 30 cm. The centre of curvature of surface is towards denser medium and a point object is placed on the principal axis in rarer medium at a distance of 15 cm from the pole of the surface. The distance of image from the pole of the surface is cm.

Q24.A capacitor of capacitance 900 µ F is charged by a 100 V battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as 𝑥× 10-2 J. The value of 𝑥 is ______.

Q24.The amplitude of a particle executing SHM is 3 cm. The displacement at which its kinetic energy will be 25% more than the potential energy is: ______ cm.

Q24.A fish rising vertically upward with a uniform velocity of 8 m s–1, observes that a bird is diving vertically downward towards the fish with the velocity of 12 m s–1. If the refractive index of water is 34 , then the actual velocity of the diving bird to pick the fish, will be __________m s−1.