Total angular momentum L = m1ω1 + m2ω2 for particles moving in the same direction.

Angular momentum about the center of mass is conserved in an elastic collision.

Since they are moving in opposite directions, the total angular momentum about point O is zero.

Total angular momentum L = m1v1r - m2v2r, but since they are in opposite directions, it simplifies to m1v1r + m2v2r.

Total angular momentum L = m1v1 + m2(-v2) = m1v1 - m2v2.

Total angular momentum is the sum of individual angular momenta, which is m1v1 + m2v2.

Angular momentum is conserved in an elastic collision about the center of mass.

Total angular momentum L = m1rω1 + m2rω2.

Angular momentum L = mvr, thus L1/L2 = (m1r1)/(m2r2) when ω is constant.

In an elastic collision, the total angular momentum about the center of mass is conserved.

The potentials due to both charges at the midpoint cancel each other, so V = 0 V.

At the midpoint, the electric fields due to both charges cancel each other out, resulting in a net electric field of 0.

The electric potential at the midpoint is zero because the potentials due to +Q and -Q cancel each other out.

At the midpoint, the potentials due to both charges cancel each other out, resulting in a net potential of 0 V.

Using the formula for parallel resistors, 1/R_eq = 1/R1 + 1/R2 = 1/4 + 1/6 = 5/12, R_eq = 12/5 = 2.4Ω.

v = √(GM/(R+h)), for h2 = 2h1, v2 = √(GM/(R+2h1)), thus v1/v2 = √(R+2h1)/(R+h1) = 1:√2.

Relative speed = 60 + 90 = 150 km/h. Time = distance/speed = 300/150 = 2 hours.

Relative speed = Speed of A + Speed of B = 60 km/h + 90 km/h = 150 km/h.

Constructive interference occurs when the phase difference between the two waves is 0 or an integer multiple of 2π.

According to the right-hand rule, the magnetic field produced by a straight current-carrying wire is perpendicular to the wire.

The magnetic field at the center of a circular loop of radius R carrying current I is given by B = μ₀I/(2R) and for a complete loop, it simplifies to B = μ₀I/(2πR).

Inside a uniformly charged cylindrical shell, the electric field is zero due to symmetry, as the contributions from all parts of the shell cancel out.

According to KCL, I = total entering - total leaving = (2A + 3A) - 5A = 0A.

According to KCL, I = Total entering - Total leaving = (3A + 2A) - 5A = 0A.

Using voltage division, V_R1 = (R1 / (R1 + R2)) * V_total = (4Ω / (4Ω + 6Ω)) * 12V = 4.8V.

Using voltage division, V_R1 = V_total * (R1 / (R1 + R2)) = 12V * (4Ω / (4Ω + 6Ω)) = 12V * (4/10) = 4.8V.

According to Kirchhoff's voltage law, the sum of the voltage drops must equal the source voltage. Here, 4V + 5V = 9V, which is correct.

Nucleotides are the building blocks of nucleic acids like DNA and RNA.

Pressure is defined as force per unit area. The dimensions of force are ML^1T^-2, and area is L^2, thus pressure has dimensions ML^-1T^-2.

The only solution is x = 0.