NTA JEE Main 13th April 2023 Shift 2

A car accelerates from rest of $$u$$ m s$$^{-1}$$. The energy spent in this process is $$E$$ J. The energy required to accelerate the car from $$u$$ m s$$^{-1}$$ to $$2u$$ m s$$^{-1}$$ is $$nE$$ J. The value of $$n$$ is _____.

A light rope is wound around a hollow cylinder of mass $$5$$ kg and radius $$70$$ cm. The rope is pulled with a force of $$52.5$$ N. The angular acceleration of the cylinder will be _____ rad s$$^{-2}$$.

Two plates A and B have thermal conductivities $$84$$ W m$$^{-1}$$ K$$^{-1}$$ and $$126$$ W m$$^{-1}$$ K$$^{-1}$$ respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of A and B are kept at $$100°$$C and $$0°$$C respectively, then the temperature of the surface of contact in steady state is _____ °C.

In an experiment with sonometer when a mass of $$180$$ g is attached to the string, it vibrates with fundamental frequency of $$30$$ Hz. When a mass $$m$$ is attached, the string vibrates with fundamental frequency of $$50$$ Hz. The value of $$m$$ is _____ g.

Three point charges $$q$$, $$-2q$$ and $$2q$$ are placed on x axis at a distance $$x = 0$$, $$x = \frac{3}{4}R$$ and $$x = R$$ respectively from origin as shown. If $$q = 2 \times 10^{-6}$$ C and $$R = 2$$ cm, the magnitude of net force experienced by the charge $$-2q$$ is _____ N.

In the circuit shown, the energy stored in the capacitor is $$n$$ $$\mu$$J. The value of $$n$$ is _____.

A straight wire AB of mass $$40$$ g and length $$50$$ cm is suspended by a pair of flexible leads in uniform magnetic field of magnitude $$0.40$$ T as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is _____ A. (Take $$g = 10$$ m s$$^{-2}$$.

An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area $$24$$ cm$$^2$$. The two ends of the wire are connected to a resistor. The total resistance in the circuit is $$12 \ \Omega$$. If an externally applied uniform magnetic field in the core along its axis changes from $$1.5$$ T in one direction to $$1.5$$ T in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be _____ mC.

A bi convex lens of focal length $$10$$ cm is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is _____ D.

An atom absorbs a photon of wavelength $$500$$ nm and emits another photon of wavelength $$600$$ nm. The net energy absorbed by the atom in this process is $$n \times 10^{-4}$$ eV. The value of $$n$$ is [Assume the atom to be stationary during the absorption and emission process] (Take $$h = 6.6 \times 10^{-34}$$ J s and $$c = 3 \times 10^8$$ m s$$^{-1}$$).