NTA JEE Main 18th March 2021 Shift 2

The velocity-displacement graph of a particle is shown in the figure.

The acceleration-displacement graph of the same particle is represented by :

If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately :
(Take : $$g = 10$$ ms$$^{-2}$$, the radius of earth, $$R = 6400 \times 10^3$$ m, Take $$\pi = 3.14$$)

A particle of mass $$m$$ moves in a circular orbit under the central potential field, $$U(r) = \frac{C}{r}$$, where $$C$$ is a positive constant. The correct radius - velocity graph of the particle's motion is :

An object of mass $$m_1$$ collides with another object of mass $$m_2$$, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses $$m_2 : m_1$$ is :

Consider a uniform wire of mass $$M$$ and length $$L$$. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is :

A solid cylinder of mass $$m$$ is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is:

[The coefficient of static friction, $$\mu_s$$, is 0.4]

The angular momentum of a planet of mass $$M$$ moving around the sun in an elliptical orbit is $$\vec{L}$$. The magnitude of the areal velocity of the planet is :

For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $$\gamma$$ is the ratio of specific heats):

An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is $$S_1$$ and that of the other part is $$S_2$$. Given that $$S_1 > S_2$$. If the piston is removed then the total entropy of the system will be:

Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root-mean-square (RMS) velocity to the average velocity of the gas molecule would be :
(Molecular weight of oxygen is 32 g mol$$^{-1}$$; $$R = 8.3$$ J K$$^{-1}$$ mol$$^{-1}$$)