NTA JEE Main 6th April 2023 Shift 2

A body is dropped on ground from a height $$h_1$$ and after hitting the ground, it rebounds to a height $$h_2$$. If the ratio of velocities of the body just before and after hitting ground is 4, then percentage loss in kinetic energy of the body is $$\dfrac{x}{4}$$. The value of $$x$$ is ______.

A ring and a solid sphere rotating about an axis passing through their centres have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is $$\sqrt{\dfrac{2}{x}}$$. The value of $$x$$ is ______.

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 $$7 \times 10^5$$ N m$$^{-2}$$. The value of mass $$m$$ is ______ kg.
(Take $$g = 9.8$$ m s$$^{-2}$$ and $$\pi = \dfrac{22}{7}$$)

A simple pendulum with length 100 cm and bob of mass 250 g is executing S.H.M of amplitude 10 cm. The maximum tension in the string is found to be $$\dfrac{x}{40}$$ N. The value of $$x$$ is ______.

Experimentally it is found that 12.8 eV energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is $$\dfrac{9}{x} \times 10^{-10}$$ m. The value of the $$x$$ is ______.
(1 eV = $$1.6 \times 10^{-19}$$ J, $$\dfrac{1}{4\pi\varepsilon_0} = 9 \times 10^9$$ $$\dfrac{Nm^2}{C^2}$$ and electronic charge = $$1.6 \times 10^{-19}$$ C)

As shown in the figure, two parallel plate capacitors having equal plate area of 200 cm$$^2$$ are joined in such a way that $$a \neq b$$. The equivalent capacitance of the combination is $$x\varepsilon_0 F$$. The value of $$x$$ is ______.

As shown in the figure below, the voltmeter reads 2 V across the 5 $$\Omega$$ resistor. The resistance of the voltmeter is ______ $$\Omega$$.

A proton with a kinetic energy of 2.0 eV moves into a region of uniform magnetic field of magnitude $$\dfrac{\pi}{2} \times 10^{-3}$$ T. The angle between the direction of magnetic field and velocity of proton is 60°. The pitch of the helical path taken by the proton is ______ cm. (Take, mass of proton = $$1.6 \times 10^{-27}$$ kg and charge on proton = $$1.6 \times 10^{-19}$$ C).

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 ______ $$\times 10^{-8}$$ H.
(Take, $$\pi^2 = 10$$)

A beam of light consisting of two wavelengths 7000 $$\mathring{A}$$ and 5500 $$\mathring{A}$$ is used to obtain interference pattern in Young's double slit experiment. The distance between the slits is 2.5 mm and the distance between the plane of slits and the screen is 150 cm. The least distance from the central fringe, where the bright fringes due to both the wavelengths coincide, is $$n \times 10^{-5}$$ m. The value of $$n$$ is ______.