NTA JEE Main 26th August 2021 Shift 2

The acceleration due to gravity is found up to an accuracy of 4% on a planet. The energy supplied to a simple pendulum of known mass $$m$$ to undertake oscillations of time period $$T$$ is being estimated. If time period is measured to an accuracy of 3%, the accuracy to which $$E$$ is known is _________ %

The coefficient of static friction between two blocks is 0.5 and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is _________ N (take $$g = 10$$ m s$$^{-2}$$)

Two simple harmonic motions are represented by the equations $$x_1 = 5\sin\left(2\pi t + \frac{\pi}{4}\right)$$ and $$x_2 = 5\sqrt{2}(\sin 2\pi t + \cos 2\pi t)$$. The amplitude of the second motion is _________ times the amplitude in the first motion.

Two waves are simultaneously passing through a string and their equations are:
$$y_1 = A_1 \sin k(x - vt)$$, $$y_2 = A_2 \sin k(x - vt + x_0)$$. Given amplitudes $$A_1 = 12$$ mm and $$A_2 = 5$$ mm, $$x_0 = 3.5$$ cm and wave number $$k = 6.28$$ cm$$^{-1}$$. The amplitude of resulting wave will be _________ mm.

If the maximum value of accelerating potential provided by a radio frequency oscillator is 12 kV. The number of revolution made by a proton in a cyclotron to achieve one sixth the speed of light is:
[$$m_p = 1.67 \times 10^{-27}$$ kg, $$e = 1.6 \times 10^{-19}$$ C, Speed of light = $$3 \times 10^8$$ m s$$^{-1}$$]

A coil in the shape of an equilateral triangle of side 10 cm lies in a vertical plane between the pole pieces of permanent magnet producing a horizontal magnetic field 20 mT. The torque acting on the coil when a current of 0.2 A is passed through it and its plane becomes parallel to the magnetic field will be $$\sqrt{x} \times 10^{-5}$$ Nm. The value of $$x$$ is _________

A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s$$^{-1}$$ in a uniform horizontal magnetic field of $$3.0 \times 10^{-2}$$ T. The maximum emf induced in the coil will be _________ $$\times 10^{-2}$$ volt (rounded off to the nearest integer).

An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal length 15 cm is placed on another side of the lens at 8 cm as shown in the figure. The image of the object coincides with the object.

When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be _________ cm

A source of light is placed in front of a screen. The intensity of light on the screen is $$I$$. Two Polaroids $$P_1$$ and $$P_2$$ are so placed in between the source of light and screen that the intensity of light on the screen is $$\frac{I}{2}$$. Then the $$P_2$$, should be rotated by an angle of _________ (degrees) so that the intensity of light on the screen becomes $$\frac{3I}{8}$$.

For the given circuit, the power across zener diode is _________ mW.