NTA JEE Main 24th January 2023 Shift 2

A body of mass 1 kg begins to move under the action of a time dependent force $$\vec{F} = (t\hat{i} + 3t^2\hat{j})$$ N, where $$\hat{i}$$ and $$\hat{j}$$ are the unit vectors along $$x$$ and $$y$$ axis. The power developed by above force, at the time $$t = 2$$ s, will be _____ W.

A uniform solid cylinder with radius $$R$$ and length $$L$$ has moment of inertia $$I_1$$, about the axis of cylinder. A concentric solid cylinder of radius $$R' = \frac{R}{2}$$ and length $$L' = \frac{L}{2}$$ is carved out of the original cylinder. If $$I_2$$ is the moment of inertia of the carved out portion of the cylinder then $$\frac{I_1}{I_2} =$$ _____.

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 $$3696 \times 10^{-x}$$ N. The value of $$x$$ is
(Given, $$g = 9.8$$ m s$$^{-2}$$ and $$\pi = \frac{22}{7}$$)

A mass $$m$$ attached to free end of a spring executes SHM with a period of 1 s. If the mass is increased by 3 kg the period of oscillation increases by one second, the value of mass $$m$$ is _____ kg.

A parallel plate capacitor with air between the plate has a capacitance of 15 pF. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant 3.5. Then the capacitance becomes $$\frac{x}{4}$$ pF. The value of $$x$$ is _____.

If a copper wire is stretched to increase its length by 20%. The percentage increase in resistance of the wire is _____%.

A single turn current loop in the shape of a right angle triangle with sides 5 cm, 12 cm, 13 cm is carrying a current of 2 A. The loop is in a uniform magnetic field of magnitude 0.75 T whose direction is parallel to the current in the 13 cm side of the loop. The magnitude of the magnetic force on the 5 cm side will be $$\frac{x}{130}$$ N. The value of $$x$$ is _____.

Three identical resistors with resistance $$R = 12$$ $$\Omega$$ and two identical inductors with self inductance $$L = 5$$ mH are connected to an ideal battery with emf of 12 V as shown in figure. The current through the battery long after the switch has been closed will be _____ A.

A convex lens of refractive index 1.5 and focal length 18 cm in air is immersed in water. The change in focal length of the lens will be _____ cm.
(Given refractive index of water = $$\frac{4}{3}$$)

The energy released per fission of nucleus of $$^{240}$$X is 200 MeV. The energy released if all the atoms in 120 g of pure $$^{240}$$X undergo fission is _____ $$\times 10^{25}$$ MeV.
(Given $$N_A = 6 \times 10^{23}$$)