NTA JEE Main 27th July 2022 Shift 1

A ball of mass $$m$$ is thrown vertically upward. Another ball of mass $$2 \text{ m}$$ is thrown at an angle $$\theta$$ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is $$\dfrac{1}{x}$$. The value of $$x$$ is ______.

A pulley of radius $$1.5 \text{ m}$$ is rotated about its axis by a force $$F = (12t - 3t^2) \text{ N}$$ applied tangentially (while $$t$$ is measured in seconds). If moment of inertia of the pulley about its axis of rotation is $$4.5 \text{ kg m}^2$$, the number of rotations made by the pulley before its direction of motion is reversed, will be $$\dfrac{K}{\pi}$$. The value of $$K$$ is ______.

A square aluminium (shear modulus is $$25 \times 10^9 \text{ N m}^{-2}$$) slab of side $$60 \text{ cm}$$ and thickness $$15 \text{ cm}$$ is subjected to a shearing force (on its narrow face) of $$18.0 \times 10^4 \text{ N}$$. The lower edge is riveted to the floor. The displacement of the upper edge is ______ $$\mu m$$.

A mass $$0.9 \text{ kg}$$, attached to a horizontal spring, executes SHM with an amplitude $$A_1$$. When this mass passes through its mean position, then a smaller mass of $$124 \text{ g}$$ is placed over it and both masses move together with amplitude $$A_2$$. If the ratio $$\dfrac{A_1}{A_2}$$ is $$\dfrac{\alpha}{\alpha - 1}$$, then the value of $$\alpha$$ will be ______.

A $$1 \text{ m}$$ long copper wire carries a current of $$1 \text{ A}$$. If the cross section of the wire is $$2.0 \text{ mm}^2$$ and the resistivity of copper is $$1.7 \times 10^{-8} \Omega \text{ m}$$. The force experienced by moving electron in the wire is ______ $$\times 10^{-23} \text{ N}$$. (Charge of electron $$= 1.6 \times 10^{-19} \text{ C}$$)

A long cylindrical volume contains a uniformly distributed charge of density $$\rho \text{ C m}^{-3}$$. The electric field inside the cylindrical volume at a distance $$x = \dfrac{2\epsilon_0}{\rho} \text{ m}$$ from its axis is ______ $$\text{V m}^{-1}$$.

In meter bridge experiment for measuring unknown resistance '$$S$$', the null point is obtained at a distance $$30 \text{ cm}$$ from the left side as shown at point $$D$$. If $$R$$ is $$5.6 \text{ k}\Omega$$, then the value of unknown resistance '$$S$$' will be ______ $$\Omega$$.

To light, a $$50 \text{ W}$$, $$100 \text{ V}$$ lamp is connected, in series with a capacitor of capacitance $$\dfrac{50}{\pi\sqrt{x}} \mu F$$, with $$200 \text{ V}$$, $$50 \text{ Hz}$$ AC source. The value of $$x$$ will be ______.

Two beams of light having intensities $$I$$ and $$4I$$ interfere to produce a fringe pattern on a screen. The phase difference between the two beams are $$\dfrac{\pi}{2}$$ and $$\dfrac{\pi}{3}$$ at points $$A$$ and $$B$$ respectively. The difference between the resultant intensities at the two points is $$xI$$. The value of $$x$$ will be ______.

The one division of main scale of Vernier callipers reads $$1 \text{ mm}$$ and $$10$$ divisions of Vernier scale is equal to the $$9$$ divisions on main scale. When the two jaws of the instrument touch each other the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between $$4.1 \text{ cm}$$ and $$4.2 \text{ cm}$$ and $$6^{th}$$ Vernier division coincides with a main scale division. The diameter of the bob will be ______ $$ 10^{-2} cm$$.