Magnitude And Directions Of A Vector

In a pn junction diode, charge carriers (electrons and holes) diffuse from areas of higher concentration to lower concentration, leading to the diffusion current. This current exists even without an external bias due to the natural movement of carriers across the junction.

The terminal velocity of a small sphere falling through a viscous medium is given by Stokes' law for low Reynolds numbers: where: - is the radius of the sphere,
- is the density of the sphere,
- is the density of the fluid,
- is the acceleration due to gravity, and
- is the dynamic viscosity of the fluid.
From this equation, we can observe that the terminal velocity is directly proportional to the square of the radius of the ball.
Thus, if the radius of the ball increases, the terminal velocity increases with the square of the radius.
Thus, the correct answer is option (C), directly proportional to the square of the radius of the ball.

Let's analyze each statement:
(A) Forces always occur in pairs:
- This is a true statement. According to Newton's Third Law, forces always occur in pairs, known as action and reaction forces, which act on different bodies but are equal in magnitude and opposite in direction.
(B) Impulsive force is a force that acts for a shorter duration:
- This is also true. Impulsive forces are forces that act over a very short time interval but cause a significant change in momentum.
(C) Impulse is the change in momentum of the body:
- This statement is true. Impulse is indeed the change in momentum of an object and is given by
, where is the change in momentum.
(D) Momentum and change in momentum both have the same direction:
- This is incorrect. Momentum is a vector quantity that depends on the velocity and direction of motion of an object. The change in momentum, however, depends on the force applied and the direction of the force. Momentum and change in momentum do not necessarily point in the same direction, especially when external forces cause a change in the direction of motion.
(E) Action and reaction forces act on different bodies:
- This is true. According to Newton's Third Law, action and reaction forces act on different bodies but are equal in magnitude and opposite in direction.
Thus, the incorrect statement is option (D), "Momentum and change in momentum both have the same direction."

The speed of a wave is related to its frequency and wavelength by the equation: where:
- is the frequency of the wave,
- is the wavelength.
Substituting the values: Now, to find the time it takes for the wave to travel a distance of 200 m, we use the equation: Substitute the values: Thus, the time taken for the wave to travel 200 m is .
Therefore, the correct answer is option (B), 0.67 s.