NTA JEE Mains 23rd Jan 2025 Shift 2

If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon =27 days and gravitational attraction between the satellite and the moon is neglected.

A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that $$\theta (t)=5t^{2}-8t$$, where $$\theta (t)$$ is the angular position of the rotating disc as a function of time t. How much power is delivered by the applied torque, when t = 2 s ?

The energy of a system is given as $$E(t)=\alpha^{3}e^{-\beta t}$$, where t is the time and $$\beta= 0.3s^{-1}$$. The errors in the measurement of $$\alpha$$ and t are 1.2% and 1.6%, respectively. At t=5s,maximum percentage error in the energy is:

Match List - I with List - II.

Choose the correct answer from the options given below :

In photoelectric effect an em-wave is incident on a metal surface and electrons are ejected from the surface. If the work function of the metal is 2.14 eV and stopping potential is 2 V , what is the wavelength of the emwave ? (Given hc = 1242eVnm where h is the Planck's constant and c is the speed of light in vaccum.)

A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance $$2.5\mu F$$. The dielectric constant of the medium between the capacitor plates is 1 . It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be _____$$Vs^{-1}$$.

In a series LCR circuit, a resistor of 300Ω, a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____$$\times 10^{4}\text{ radians }s^{-1}$$

An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension $$0.095 J/m^{2}$$ and density $$10^{3}kg/m^{3}$$. The difference between pressure inside the bubble and atmospheric pressure is _____$$N/m^{2}.(\text{ take }g=10m/s^{2})$$

A satellite of mass $$\frac{M}{2}$$ is revolving around earth in a circular orbit at a height of $$\frac{R}{3}$$ from earth surface. The angular momentum of the satellite is $$M\sqrt{\frac{GMR}{x}}$$.The value of $$x$$ is ______ , where M and R are the mass and radius of earth, respectively. ( G is the gravitational constant)

At steady state the charge on the capacitor, as shown in the circuit below, is $$\mu C$$.