NTA JEE Main 6th September 2020 Shift 2 - Physics

A particle moving in the xy-plane experiences a velocity dependent force $$\vec{F} = k(v_y\hat{i} + v_x\hat{j})$$, where $$v_x$$ and $$v_y$$ are the x and y components of its velocity $$\vec{v}$$. If $$\vec{a}$$ is the acceleration of the particle, then which of the following statements is true for the particle?

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed $$v$$, he sees that rain drops coming at an angle $$60^\circ$$ from the horizontal. On further increasing the speed of the car to $$(1+\beta)v$$, this angle changes to $$45^\circ$$. The value of $$\beta$$ is close to:

Particle A of mass $$m_1$$ moving with velocity $$(\sqrt{3}\hat{i} + \hat{j})\,\text{ms}^{-1}$$ collides with another particle B of mass $$m_2$$ which is at rest initially. Let $$\vec{v}_1$$ and $$\vec{v}_2$$ be the velocities of particles A and B after collision respectively. If $$m_1 = 2m_2$$ and after collision $$\vec{v}_1 - (\hat{i} + \sqrt{3}\hat{j})\,\text{ms}^{-1}$$, the angle between $$\vec{v}_1$$ and $$\vec{v}_2$$ is:

The linear mass density of a thin rod AB of length L varies from A to B as $$\lambda(x) = \lambda_0\left(1 + \frac{x}{L}\right)$$, where $$x$$ is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is:

Two planets have masses M and 16M and their radii are $$a$$ and $$2a$$, respectively. The separation between the centres of the planets is $$10a$$. A body of mass $$m$$ is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firing speed needed is:

A fluid is flowing through a horizontal pipe of varying cross-section, with speed $$v\,\text{ms}^{-1}$$ at a point where the pressure is P Pascal. At another point where pressure is $$\frac{P}{2}$$ Pascal its speed is $$V\,\text{ms}^{-1}$$. If the density of the fluid is $$\rho\,\text{kg m}^{-3}$$ and the flow is streamline, then $$V$$ is equal to:

Three rods of identical cross-section and length are made of three different materials of thermal conductivity $$K_1$$, $$K_2$$ and $$K_3$$, respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at $$100^\circ\text{C}$$ and the other at $$0^\circ\text{C}$$ (see figure). If the joints of the rod are at $$70^\circ\text{C}$$ and $$20^\circ\text{C}$$ in steady state and there is no loss of energy from the surface of the rod, the correct relationship between $$K_1$$, $$K_2$$ and $$K_3$$ is:

In a dilute gas at pressure P and temperature 't', the time between successive collision of a molecule varies with T as:

Assuming the nitrogen molecule is moving with r.m.s. velocity at 400 K, the de-Broglie wave length of nitrogen molecule is close to: (Given: nitrogen molecule weight: $$4.64 \times 10^{-26}\,\text{kg}$$, Boltzman constant: $$1.38 \times 10^{-23}\,\text{J K}^{-1}$$, Planck constant: $$6.63 \times 10^{-34}\,\text{J s}$$)

When a particle of mass $$m$$ is attached to a vertical spring of spring constant $$k$$ and released, its motion is described by $$y(t) = y_0\sin^2\omega t$$, where 'y' is measured from the lower end of unstretched spring. Then $$\omega$$ is:

Two identical electric point dipoles have dipole moments $$\vec{p}_1 = p\hat{i}$$ and $$\vec{p}_2 = -p\hat{i}$$ and are held on the x-axis at distance 'a' from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is 'm', their speed when they are infinitely far apart is:

Consider the force F on a charge 'q' due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F, if 'q' is placed at distance r from the centre of the shell?

In the figure shown, the current in the $$10\,\text{V}$$ battery is close to:

A circuit to verify Ohm's law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In the circuit:

A charged particle going around in a circle can be considered to be a current loop. A particle of a mass $$m$$ carrying charge $$q$$ is moving in a plane with speed $$v$$ under the influence of magnetic field $$\vec{B}$$. The magnetic moment of this moving particle is:

A square loop of side $$2a$$ and carrying current I is kept in xz plane with its centre at origin. A long wire carrying the same current I is placed parallel to z-axis and passing through point $$(0, b, 0)$$, $$(b >> a)$$. The magnitude of torque on the loop about z-axis will be:

For a plane electromagnetic wave, the magnetic field at a point x and time t is:
$$\vec{B}(x, t) = [1.2 \times 10^{-7}\sin(0.5 \times 10^3 x + 1.5 \times 10^{11}t)\hat{k}]\,\text{T}$$.
The instantaneous electric field $$\vec{E}$$ corresponding to $$\vec{B}$$ is:

A double convex lens has power P and same radii of curvature R of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power $$1.5\,P$$ is:

Given the masses of various atomic particles $$m_P = 1.0072\,\text{u}$$, $$m_n = 1.0087\,\text{u}$$, $$m_e = 0.000548\,\text{u}$$, $$m_{\bar{v}} = 0$$, $$m_d = 2.0141\,\text{u}$$, where p = proton, n = neutron, e = electron, $$\bar{v}$$ = antineutrino and d = deuteron. Which of the following process is allowed by momentum and energy conservation:

A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings 5.50 mm, 5.55 mm, 5.34 mm, 5.65 mm. The average of these four readings is 5.5375 mm and the standard deviation of the data is 0.07395 mm. The average diameter of the pencil should therefore be recorded as:

The centre of mass of a solid hemisphere of radius $$8\,\text{cm}$$ is $$x\,\text{cm}$$ from the centre of the flat surface. Then value of $$x$$ is___

An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to___

In a series LR circuit, power of $$400\,\text{W}$$ is dissipated from a source of $$250\,\text{V}$$, $$50\,\text{Hz}$$. The power factor of the circuit is $$0.8$$. In order to bring the power factor to unity, a capacitor of value C is added in series to the L and R. Taking the value of C as $$\left(\frac{n}{3\pi}\right)\,\mu F$$, then value of n is___

A Young's double-slit experiment is performed using monochromatic light of wavelength $$\lambda$$. The intensity of light at a point on the screen, where the path difference is $$\lambda$$, is $$K$$ units. The intensity of light at a point where the path difference is $$\dfrac{\lambda}{6}$$ is given by $$\dfrac{nK}{12}$$, where n is an integer. The value of n is___

The output characteristics of a transistor is shown in the figure. When $$V_{CE}$$ is $$10\,\text{V}$$ and $$I_C = 4.0\,\text{mA}$$, then value of $$\beta_{ac}$$ is___