NTA JEE Main 16th March 2021 Shift 2 - Physics

In order to determine the Young's Modulus of a wire of radius 0.2 cm (measured using a scale of least count = 0.001 cm) and length 1 m (measured using a scale of least count = 1 mm), a weight of mass 1 kg (measured using a scale of least count = 1 g) was hanged to get the elongation of 0.5 cm (measured using a scale of least count 0.001 cm). What will be the fractional error in the value of Young's Modulus determined by this experiment?

A mosquito is moving with a velocity $$\vec{v} = 0.5t^2\hat{i} + 3t\hat{j} + 9\hat{k}$$ m s$$^{-1}$$ and accelerating in uniform conditions. What will be the direction of mosquitoes after 2 s?

Statement I: A cyclist is moving on an unbanked road with a speed of 7 km h$$^{-1}$$ and takes a sharp circular turn along a path of the radius of 2 m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve ($$g = 9.8$$ m s$$^{-2}$$).
Statement II: If the road is banked at an angle of 45°, cyclist can cross the curve of 2 m radius with the speed of 18.5 km h$$^{-1}$$ without slipping. In the light of the above statements, choose the correct answer from the options given below.

A large block of wood of mass $$M = 5.99$$ kg is hanging from two long massless cords. A bullet of mass $$m = 10$$ g is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their center of mass rising a vertical distance $$h = 9.8$$ cm before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before the collision is: (Take $$g = 9.8$$ m s$$^{-2}$$)

What will be the nature of flow of water from a circular tap, when its flow rate increased from 0.18 L (min)$$^{-1}$$ to 0.48 L (min)$$^{-1}$$? The radius of the tap and viscosity of water are 0.5 cm and $$10^{-3}$$ Pa s, respectively. (Density of water: $$10^{3}$$ kg m$$^{-3}$$)

A bimetallic strip consists of metals $$A$$ and $$B$$. It is mounted rigidly as shown. The metal $$A$$ has higher coefficient of expansion compared to that of metal $$B$$. When the bimetallic strip is placed in a cold bath, it will:

Calculate the value of the mean free path ($$\lambda$$) for oxygen molecules at temperature 27°C and pressure $$1.01 \times 10^{5}$$ Pa. Assume the molecular diameter 0.3 nm and the gas is ideal. ($$k = 1.38 \times 10^{-23}$$ J K$$^{-1}$$)

The amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500 g, Decay constant = 20 g s$$^{-1}$$ then how much time is required for the amplitude of the system to drop to half of its initial value? ($$\ln 2 = 0.693$$)

Find out the surface charge density at the intersection of point $$x = 3$$ m plane and $$x$$-axis, in the region of uniform line charge of 8 nC m$$^{-1}$$ lying along the $$z$$-axis in free space.

A resistor develops 500 J of thermal energy in 20 s when a current of 1.5 A is passed through it. If the current is increased from 1.5 A to 3 A, what will be the energy developed in 20 s.

A charge $$Q$$ is moving $$d\vec{l}$$ distance in the magnetic field $$\vec{B}$$. Find the value of work done by $$\vec{B}$$.

The magnetic field in a region is given by $$\vec{B} = B_0\left(\frac{x}{a}\right)\hat{k}$$. A square loop of side $$d$$ is placed with its edges along the $$x$$ and $$y$$ axes. The loop is moved with a constant velocity $$\vec{v} = v_0\hat{i}$$. The emf induced in the loop is:

For the given circuit, comment on the type of transformer used:

Red light differs from blue light as they have:

The refractive index of a converging lens is 1.4. What will be the focal length of this lens if it is placed in a medium of same refractive index? (Assume the radii of curvature of the faces of lens are $$R_1$$ and $$R_2$$ respectively)

The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100 V. What should nearly be the ratio of their wavelengths? ($$m_p = 1.00727$$ u, $$m_e = 0.00055$$ u)

The half-life of $$Au^{198}$$ is 2.7 days. The activity of 1.50 mg of $$Au^{198}$$, if its atomic weight is 198 g mol$$^{-1}$$ is, ($$N_A = 6 \times 10^{23}$$ mol$$^{-1}$$)

Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 min.

The following logic gate is equivalent to:

Two identical antennas mounted on identical towers are separated from each other by a distance of 45 km. What should nearly be the minimum height of receiving antenna to receive the signals in line of sight? (Assume radius of earth is 6400 km)

A body of mass 2 kg moves under a force of $$\left(2\hat{i} + 3\hat{j} + 5\hat{k}\right)$$ N. It starts from rest and was at the origin initially. After 4 s, its new coordinates are $$(8, b, 20)$$. The value of $$b$$ is ________. (Round off to the Nearest Integer)

A swimmer can swim with velocity of 12 km/h in still water. Water flowing in a river has velocity 6 km/h. The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ________°. (Round off to the Nearest Integer) (find the angle in degree)

A force $$\vec{F} = 4\hat{i} + 3\hat{j} + 4\hat{k}$$ is applied on an intersection point of $$x = 2$$ plane and $$x$$-axis. The magnitude of torque of this force about a point $$(2, 3, 4)$$ is ________. (Round off to the Nearest Integer)

A solid disc of radius $$a$$ and mass $$m$$ rolls down without slipping on an inclined plane making an angle $$\theta$$ with the horizontal. The acceleration of the disc will be $$\frac{2}{b}g\sin\theta$$, where $$b$$ is ________. (Round off to the Nearest Integer) ($$g$$ = acceleration due to gravity, $$\theta$$ = angle as shown in figure)

If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be $$\frac{x}{5}\frac{GM^2}{R}$$ where $$x$$ is ________. (Round off to the Nearest Integer)
($$M$$ is the mass of earth, $$R$$ is the radius of earth, $$G$$ is the gravitational constant)

For an ideal heat engine, the temperature of the source is 127°C. In order to have 60% efficiency the temperature of the sink should be ________°C. (Round off to the nearest integer)

A closed organ pipe of length $$L$$ and an open organ pipe contain gases of densities $$\rho_1$$ and $$\rho_2$$ respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is $$\frac{x}{3}L\sqrt{\frac{\rho_1}{\rho_2}}$$, where $$x$$ is ________. (Round off to the Nearest Integer)

In a parallel plate capacitor set up, the plate area of capacitor is 2 m$$^2$$ and the plates are separated by 1 m. If the space between the plates are filled with a dielectric material of thickness 0.5 m and are 2 m$$^2$$ (see figure) the capacitance of the set-up will be $$\varepsilon_0$$ ________.
(Dielectric constant of the material = 3.2) (Round off to the Nearest Integer)

The energy dissipated by a resistor is 10 mJ in 1 s, when an electric current of 2 mA flows through it. The resistance is ________ $$\Omega$$. (Round off to the Nearest Integer)

A deviation of 2° is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass are 0.02 and 0.03 respectively and refractive index for yellow light for these glasses are 1.5 and 1.6 respectively. The refracting angles for crown glass prism will be ________° (in degree). (Round off to the Nearest Integer)