NTA JEE Main 28th July 2022 Shift 2

In an experiment to find acceleration due to gravity $$g$$ using simple pendulum, time period of 0.5 s is measured from time of 100 oscillation with a watch of 1 s resolution. If measured value of length is 10 cm known to 1 mm accuracy. The accuracy in the determination of $$g$$ is found to be $$x\%$$. The value of $$x$$ is

A ball is thrown vertically upwards with a velocity of 19.6 m s$$^{-1}$$ from the top of a tower. The ball strikes the ground after 6 s. The height from the ground up to which the ball can rise will be $$\frac{k}{5}$$ m. The value of $$k$$ is _____ (use $$g = 9.8 \ m s^{-2}$$)

The distance of centre of mass from end A of a one dimensional rod (AB) having mass density $$\rho = \rho_0\left(1 - \frac{x^2}{L^2}\right)$$ kg m$$^{-1}$$ and length $$L$$ (in meter) is $$\frac{3L}{\alpha}$$ m. The value of $$\alpha$$ is _____ (where $$x$$ is the distance from end A)

A string of area of cross-section 4 mm$$^2$$ and length 0.5 is connected with a rigid body of mass 2 kg. The body is rotated in a vertical circular path of radius 0.5 m. The body acquires a speed of 5 m s$$^{-1}$$ at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is _____ $$\times 10^{-5}$$. (Use Young's modulus $$10^{11}$$ N m$$^{-2}$$ and $$g = 10 \ m s^{-2}$$)

At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be _____ J.

The potential energy of a particle of mass 4 kg in motion along the x-axis is given by $$U = 4(1 - \cos 4x)$$ J. The time period of the particle for small oscillation $$(\sin\theta \approx \theta)$$ is $$\frac{\pi}{K}$$ s. The value of $$K$$ is _____

An electrical bulb rated 220 V, 100 W, is connected in series with another bulb rated 220 V, 60 W. If the voltage across combination is 220 V, the power consumed by the 100 W bulb will be about _____ W.

For the given circuit the current through battery of 6 V just after closing the switch 'S' will be _____ A.

An object 'O' is placed at a distance of 100 cm in front of a concave mirror of radius of curvature 200 cm as shown in the figure. The object starts moving towards the mirror at a speed 2 cm s$$^{-1}$$. The position of the image from the mirror after 10 s will be at _____ cm.

In an experiment with a convex lens, the plot of the image distance ($$v'$$) against the object distance ($$\mu'$$) measured from the focus gives a curve $$v'\mu' = 225$$. If all the distances are measured in cm. The magnitude of the focal length of the lens is _____ cm.