Practice Questions

Q7. A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be ______ m s−1 .

Q7. A circular plate is rotating in horizontal plane, about an axis passing through its centre and perpendicular to the plate, with an angular velocity ω. A person sits at the centre having two dumbbells in his hands. When he stretched out his hands, the moment of inertia of the system becomes triple. If E be the initial Kinetic energy of the system, then final Kinetic energy will be E . The value of x is x

Q7. Two discs of same mass and different radii are made of different materials such that their thicknesses are 1 cm and 0. 5 cm respectively. The densities of materials are in the ratio 3 : 5 . The moment of inertia of these discs respectively about their diameters will be in the ratio of x . The value of x is ______. 6

Q7. A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is π : 22 then, the value of its angular speed will be _________rad s−1. JEE Main 2023 (13 Apr Shift 1) JEE Main Previous Year Paper

Q7. ICM is moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. IAB is its moment of inertia about an axis AB perpendicular to plane and parallel to axis CM at a distance 2 R from center, where R is the radius of the disc. The ratio of IAB and ICM is x : 9. The value of x is 3 ______.

Q7. Given below are two statements: Statement I: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface. JEE Main 2023 (24 Jan Shift 2) JEE Main Previous Year Paper Statement II: Acceleration due to earth's gravity is same at a height ' h' and depth ' d' from earth's surface, if h = d. In the light of above statements, choose the most appropriate answer form the options given below (1) Statement I is incorrect but statement II is correct (2) Both Statement I and Statement II are incorrect (3) Statement I is correct but statement II is incorrect (4) Both Statement I and II are correct

Q8. A uniform disc of mass 0. 5 kg and radius r is projected with velocity 18 m s−1 at t = 0 s on a rough horizontal surface. It starts off with a purely sliding motion at t = 0 s. After 2 s it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after 2 s will be ______ J. (given, coefficient of friction is 0. 3 and g = 10 m s−2 ).

Q8. Given below are two statements: Statement I: The temperature of a gas is -73 °C. When the gas is heated to 527 °C, the root mean square speed of the molecules is doubled. Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the options given below: (1) Both Statement I and Statement II are true (2) Statement I is true but Statement II is false (3) Both Statement I and Statement II are false (4) Statement I is false but Statement II is true

Q9. A metal block of mass m is suspended from a rigid support through a metal wire of diameter 14 mm. The tensile stress developed in the wire under equilibrium state is 7 × 105 N m–2 . The value of mass m is ______ kg. (Take g = 9. 8 m s−2 and π = 227 )

Q10.A body cools from 60°C to 40°C in 6 minutes. If, temperature of surroundings is 10°C . Then, after the next 6 minutes, its temperature will be ______ °C.

Q10.A steel rod of length 1 m and cross-sectional area 10−4 m2 is heated from 0°C to 200°C without being allowed to extend or bend. The compressive tension produced in the rod is _____ ×104 N . (Given Young's modulus of steel = 2 × 1011 N m−2 , coefficient of linear expansion = 10−5 K−1 )

Q10.A faulty thermometer reads 5°C in melting ice and 95°C in steam. The correct temperature on absolute scale will be ______ K when the faulty thermometer reads 41°C.

Q10.A spherical drop of liquid splits into 1000 identical spherical drops. If ui is the surface energy of the original = ( 10x ). Then drop and uf is the total surface energy of the resulting drops, the (ignoring evaporation), ufui value of x is ______:

Q10.If two charges 𝑞1and 𝑞2 are separated with distance 𝑑 and placed in a medium of dielectric constant 𝑘. What will be the equivalent distance between charges in air for the same electrostatic force? (1) 𝑑√𝑘 (2) 𝑘√𝑑 (3) 1 . 5𝑑√𝑘 (4) 2𝑑√𝑘

Q10.The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J. The cross sectional area of the wire is _____ mm2. (Given, Y = 2. 0 × 1011 N m–2 )

Q10.As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45° with the load axis. The length of wire is 62. 8 cm and its diameter is 4 mm. The Young's modulus is found to be x × 104 N m−2 The value of x is _______.

Q10.A water heater of power 2000 W is used to heat water. The specific heat capacity of water is 4200 J kg−1 K−1 . The efficiency of heater is 70%. Time required to heat 2 kg of water from 10°C to 60°C is _____ s . (Assume that the specific heat capacity of water remains constant over the temperature range of the water).

Q10.Glycerin of density 1. 25 × 103 kg m–3 is flowing through the conical section of pipe. The area of cross- section of the pipe at its ends are 10 cm2 and 5 cm2 and pressure drop across its length is 3 N m–2 . The rate of flow of glycerine through the pipe is x × 10–5 m3 s–1 . The value of x is _____.

Q10.The surface tension of soap solution is 3. 5 × 10−2 N m−1 . The amount of work done required to increase the radius of soap bubble from 10 cm to 20 cm is _____ ×10−4 J . (take π = 227 )

Q11.A metal block of base area 0. 20 m2 is placed on a table, as shown in figure. A liquid film of thickness 0. 25 mm is inserted between the block and the table. The block is pushed by a horizontal force of 0. 1 N and moves with a constant speed. If the viscosity of the liquid is 5. 0 × 10–3 Pl, the speed of block is ______ ×10−3 m s−1 .

Q11.A parallel plate capacitor of capacitance 2 F is charged to a potential 𝑉. The energy stored in the capacitor is 𝐸1. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The 𝐸2 energy stored in the combination is 𝐸2. The ratio is 𝐸1 (1) 2: 1 (2) 2: 3 (3) 1: 2 (4) 1: 4

Q11.A spherical ball of radius 1 mm and density 10. 5 g cc−1 is dropped in glycerine of coefficient of viscosity 9. 8 poise and density 1. 5 g cc−1 . Viscous force on the ball when it attains constant velocity is 3696 × 10−x N . The value of x is (Given, g = 9. 8 m s−2 and π = 227 )

Q11.As shown in the figure, a network of resistors is connected to a battery of 24 V with an internal resistance of 3 𝛺. The currents through the resistors 𝑅4 and 𝑅5 are 𝐼4 and 𝐼5 respectively. The values of 𝐼4 and 𝐼5 are: 8 2 24 6 (1) 𝐼4 = 5 A and I5 = 5 A (2) 𝐼4 = 5 A and 𝐼5 = 5 A (3) 𝐼4 = 6 A and 𝐼5 = 24 A (4) 𝐼4 = 2 A and 𝐼5 = 8 A 5 5 5 5

Q11.A body cools from 80oC to 60o in 5 minutes. The temperature for the surrounding is 20oC. The time it takes to cool from 60oC to 40oC is (1) 450 s (2) 420 s (3) 500 s (4) 253 s

Q11.The surface of water in a water tank of cross section area 750 cm2 on the top of a house is h m. above the tap level. The speed of water coming out through the tap of cross section area 500 mm2 is 30 cm s−1 . At that instant, dh is x × 10−3 m s−1 . The value of x will be ______. dt