IIT-JAM 2019/Physics Q.31(MSQ) Ans - (A,B)

Solution -

Option A states that the central density of nuclei is independent of A, which is true. let see how -

Density = Mass/Volume

Mass = mass number (A) ✕ mass of one nucleon(u = 1.67 ✕ 10^-27 kg)

Volume = 4/3π (R)^3 = 4/3 π (1.2 A^1/3 fm )^3 [GIVEN- R=1.2 A^1/3 fm]

Density = A.u/4/3 π (1.2 A^1/3 fm )^3

= u/4/3 π (1.2 fm )^3

Now, we can clearly see that density is a constant term and not dependent on the mass number - A.

Option B states that the volume-energy per nucleon is constant, which is true. let see how -

Volume energy(Ev) ∝ Mass number(A)

Ev = k.A (where k is constant)

Volume energy for 1 nucleon(1 nucleon = 1 proton or 1 neutron), Ev = k [A=1]

The volume-energy per nucleon is constant.

Option C states that the attractive part of the nuclei force has a long-range, which is false.

Nuclear forces are short-range forces. It is powerfully attractive at a distance of 1 femtometre (fm) and then rapidly decreases.

Option D states that the nuclear force is charge-dependent, which is false.

In nuclei, nuclear force is independent of whether the nucleons are proton or neutron.

Ans (C)

First of all, we need to know what is Coriolis force,

On a rotating body, if an object wants to move in a straight line, it gets deflected by his path. And this is because of Coriolis's force or effect.

Let understand with an example - Earth,

If you want to move from point A to B(long-distance) in a straight line on earth northern or southern hemisphere, Coriolis force or effect makes your path to appear to oppose your straight path by a deflection(say to the point as c).

This force on Earth lies in the view of the fact that the Earth has different speeds in its different latitudes. The Earth equator moves at a high-speed 1040mph, and if we move farther from the equator, it's speed decreases.

Note - you are not actually deviating from the straight path, but it appears to do so because of the motion of the coordinate system.

Now a perfect physics definition,

The Coriolis force is a pseudo force that acts on objects that are in motion within a non-inertial frame of reference that rotates concerning an inertial frame.

Now, coming to our exam question, we need to find the direction of Coriolis force -

Coriolis force(F) = - 2m(vector-ω ⨯ vector-v)

By using the right-hand thumb rule, the direction will be perpendicular to both velocities.

ANS - (A,B,C)

The gradient of a scalar field is a measure of the maximum rate of change in that scalar field, and it is a vector quantity.
If Φ(x, y) is a function, then the gradient is given by
Now, let see another function f(x, y){suppose}

And if it's line integral of the gradient is given -

You can see that the line integral of the gradient is only dependent on its points, not on the path. And if it is a closed line integral, then the starting and endpoint will same, and the resultant will be zero.

ANS - (A,C)

Sol -
A.

C

ANS- (C)

There is two frame reference.

1. Inertial frame of reference (a = 0)  {acceleration}

2. Non-Inertial frame of reference (a ≠ 0)

We know that newton's laws of motion are strictly valid only for the Inertial frame of reference. Newton laws are also accurate in the reference frame, which is in uniform motion with respect to the Inertial frame of reference.

So the Galilean transformation is used to transform between the coordinates of two reference frames, which has the only difference of constant relative motion.

But when maxwell gives his equation, there is a term called c (speed of light).

So, Galilean transformation says when you(observer in Inertial frame of reference) notice the light(emitting from a light source in the uniform inertial frame of reference). Its speed would be V+C(light speed), which is not possible since we know the light is the fastest in the universe.

So, for this problem, physicists develop Lorentz transformation, which is valid for maxwell equations.