NTA JEE Main 6th September 2020 Shift 1 - Physics

A clock has a continuously moving second's hand of $$0.1\,\text{m}$$ length. The average acceleration of the tip of the hand (in units of $$\text{ms}^{-2}$$) is of the order of:

An insect is at the bottom of a hemispherical ditch of radius $$1\,\text{m}$$. It crawls up the ditch but starts slipping after it is at height $$h$$ from the bottom. If the coefficient of friction between the ground and the insect is $$0.75$$, then $$h$$ is: $$(g = 10\,\text{m s}^{-2})$$

If the potential energy between two molecules is given by $$U = \frac{A}{r^6} + \frac{B}{r^{12}}$$, then at equilibrium, separation between molecules, and the potential energy are:

Shown in the figure is a hollow ice-cream cone (it is open at top). If its mass is M, radius of its top is R and height, H, then its moment of inertia about its axis is:

Four point masses, each of mass $$m$$, are fixed at the corners of a square of side $$l$$. The square is rotating with angular frequency $$\omega$$, about an axis passing through one of the corners of the square and parallel to its diagonal, as shown in the figure. The angular momentum of the square about the axis is:

A satellite is in an elliptical orbit around a planet $$P$$. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is:

Molecules of an ideal gas are known to have three translational degrees of freedom. The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of $$\gamma = \left(\frac{C_p}{C_v}\right)$$ are given, respectively, by:

An object of mass $$m$$ is suspended at the end of a massless wire of length $$L$$ and area of cross-section, A. Young modulus of the material of the wire is $$Y$$. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is:

A sound source S is moving along a straight track with speed $$v$$, and is emitting sound of frequency $$v_0$$. An observer is standing at a finite distance, at the point O, from the track. The time variation of frequency heard by the observer is best represented by: ($$t_0$$ represents the instant when the distance between the source and observer is minimum)

Charges $$Q_1$$ and $$Q_2$$ are at points A and B of a right-angled triangle OAB. The resultant electric field at point O is perpendicular to the hypotenuse, then $$Q_1/Q_2$$ is proportional to:

For the given input voltage waveform $$V_{in}(t)$$, the output voltage waveform $$V_0(t)$$, across the capacitor is correctly depicted by:

A particle of charge $$q$$ and mass $$m$$ is moving with a velocity $$-v\hat{i}$$ $$(v \neq 0)$$ towards a large screen placed in the $$Y-Z$$ plane at distance $$d$$. If there is a magnetic field $$\vec{B} = B_0\hat{k}$$, the minimum value of $$v$$ for which the particle will not hit the screen is:

An electron is moving along $$+x$$ direction with a velocity of $$6 \times 10^6\,\text{ms}^{-1}$$. It enters a region of uniform electric field of $$300\,V/cm$$ pointing along $$+y$$ direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the $$x$$ direction will be:

An AC circuit has $$R = 100\,\Omega$$, $$C = 2\,\mu F$$ and $$L = 80\,\text{mH}$$, connected in series. The quality factor of the circuit is:

A point like object is placed at distance of $$1\,\text{m}$$ in front of a convex lens of focal length $$0.5\,\text{m}$$. A plane mirror is placed at a distance of $$2\,\text{m}$$ behind the lens. The position and nature of the image formed by the system is:

In the figure below, $$P$$ and $$Q$$ are two equally intense coherent sources emitting radiation of wavelength $$20\,\text{m}$$. The separation between P and Q is $$5\,\text{m}$$ and the phase of P is ahead of that of Q by $$90^\circ$$. A, B and C are three distinct point of observation, each equidistant from the midpoint of PQ. The intensities of radiation at A, B, C will be in the ratio:

An electron, a doubly ionized helium ion $$(He^{++})$$ and proton are having the same kinetic energy. The relation between their respective de-Broglie wavelength $$\lambda_e$$, $$\lambda_{He^{++}}$$ and $$\lambda_p$$ is:

You are given that $$^7_3\text{Li} = 7.0160\,\text{u}$$, Mass of $$^4_2\text{He} = 4.0026\,\text{u}$$ and Mass of $$^1_1\text{He} = 1.0079\,\text{H}$$. When $$20\,\text{g}$$ of $$^7_3\text{Li}$$ is converted into $$^4_2\text{He}$$ by proton capture, the energy liberated, (in kWh), is: [Mass of nucleon $$= 1\,\text{GeV}/c^2$$]

Identify the correct output signal $$Y$$ in the given combination of gates (as shown $$n$$) for the given inputs $$A$$ and $$B$$:

A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of $$0.5\,\text{mm}$$ is noticed on the pitch scale. The nature of zero error involved and the least count of the screw gauge, are respectively:

The density of a solid metal sphere is diameter. The maximum error in the density of the sphere is $$\left(\frac{x}{100}\right)\%$$. If the relative errors in measuring the mass and the diameter are $$6.0\%$$ and $$1.5\%$$ respectively, the value of $$x$$ is ___

Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial velocities of the two bodies (in degree) is ___

Initially a gas of diatomic molecules is contained in a cylinder of volume $$V_1$$ at a pressure $$P_1$$ and temperature $$250\,\text{K}$$. Assuming that $$25\%$$ of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature $$2000\,\text{K}$$, when contained in a volume $$2V_1$$ is given by $$P_2$$. The ratio $$P_2/P_1$$ is ___

Suppose that intensity of a laser is $$\left(\frac{315}{\pi}\right)\,\text{W m}^{-2}$$. The rms electric field, in units of $$\text{V m}^{-1}$$ associated with this source is close to the nearest integer is ___ ($$\varepsilon_0 = 8.86 \times 10^{-12}\,\text{C}^2\,\text{N m}^{-2}$$; $$c = 3 \times 10^8\,\text{m s}^{-1}$$)

A part of a complete circuit is shown in the figure. At some instant, the value of current I is $$1\,\text{A}$$ and it is decreasing at a rate of $$10^2\,\text{As}^{-1}$$. The value of the potential difference $$V_P - V_Q$$, (in volts) at that instant is___