Which fundamental physical quantity is defined by taking the fixed numerical value of the elementary charge (e) to be 1.602176634×10⁻¹⁹ C, where the second is defined in terms of Δν_cs?

If we test the dimensional consistency of the kinematic equation x = x₀ + v₀ t + (1/2) a t², what is the dimension of the term (1/2) a t²?

The magnitude of force needed to hold a 0.25 kg stone whirling in a horizontal circle of radius 1.5 m is limited by a maximum tension of 200 N. What is the maximum speed (v) the stone can be whirled at before the string breaks?

The position of an object moving along the x-axis is given by x = a + b t², where a = 8.5 m and b = 2.5 m s⁻². What is the average velocity between t = 2.0 s and t = 4.0 s?

In Galileo's law of odd numbers describing free fall, the distances traversed during successive equal intervals of time (τ) stand to one another in what ratio?

An object is thrown vertically upwards from a building top 25.0 m above the ground with an initial velocity of 20 m s⁻¹. Taking g = 10 m s⁻², what is the total time the ball is in flight before it hits the ground?

What physical quantity is represented by the area under the velocity-time (v-t) curve over a given time interval?

The path of a projectile launched with initial velocity v₀ at angle θ₀, neglecting air resistance, follows the equation y = a x + b x². This means the path is a:

For a projectile launched with initial velocity v₀ at angle θ₀, the maximum height (hm) reached is given by the formula:

The horizontal range (R) of a projectile is given by R = (v₀² sin 2θ₀) / g. For a given projection speed v₀, the range is maximum when sin 2θ₀ is maximum. What angle θ₀ maximizes the range?

Rain falls vertically at 35 m s⁻¹. Wind blows horizontally from east to west at 12 m s⁻¹. Using the vector addition rule, what is the magnitude of the resultant velocity (R) of the rain?

A heavy wooden block is placed on a soft horizontal floor. When an iron cylinder is placed on top of the block, the system (block + cylinder) accelerates downwards with 0.1 m s⁻². The total mass of the system is 27 kg. If g = 10 m s⁻², what is the magnitude of the normal force (R') exerted by the floor on the system?

When a force is applied for a certain time interval on two bodies of different masses, initially at rest, what fundamental observation related to momentum change is made?

Which statement accurately describes the characteristics of static friction (fs)?

An object of mass m moving with initial speed u is subjected to a constant retarding force F_R. What expression gives the time t required for the object to come to rest?

The total mechanical energy (E = K + V) of a system is conserved if which condition holds true for the forces doing work on the system?

If a force F acts on an object over a displacement d, and the angle between F and d is θ, the work done W is mathematically defined as the scalar product:

If A is the area of the circle swept by a windmill and v is the wind velocity perpendicular to the circle, the kinetic energy of the air passing through in time t has dimensions of:

Consider an elastic collision in one dimension between two identical masses (m₁ = m₂). If mass m₂ is initially at rest and m₁ strikes it with velocity v₁i, what is the final velocity of m₁ (v₁f)?

A rigid body which is pivoted or fixed in some way can only have:

If three particles of equal mass form a triangle, their center of mass coincides with the:

If F_ext= 0 for a system of particles, which quantity is conserved, implying the center of mass moves uniformly in a straight line?

Kepler’s Law of Areas sweeping equal areas in equal time intervals is a direct consequence of the conservation of:

The vector form of Newton’s Universal Law of Gravitation for the attractive force F on m₂ due to m₁, where r̂ is the unit vector from m₁ to m₂, is:

The angular momentum l of a single particle with respect to the origin O is defined by the vector product:

The gravitational force of attraction due to a hollow spherical shell of uniform density, on a point mass situated inside it, is:

In the Cavendish experiment to measure G, the gravitational torque produced by the large spheres on the small spheres is balanced by the:

If the gravitational potential energy V is chosen to be zero as r → ∞, the gravitational potential energy associated with two particles of mass m₁ and m₂ separated by distance r is:

For a satellite of mass m in a circular orbit of radius a around a massive body M, the total energy E is related to its kinetic energy K by:

The property of a body that causes it to regain its original size and shape upon removal of the applied force is called:

The SI unit and dimensional formula for stress are:

Longitudinal strain (ε) for a body under tensile or compressive stress is defined as:

When a cylinder is subjected to tangential forces resulting in a relative displacement Δx, the shearing strain is defined as Δx / L. For small angular displacement θ, this strain is approximately:

The strain produced when a body is under hydraulic compression uniform pressure applied perpendicularly everywhere on the surface is called:

For small deformations within the elastic limit, Hooke’s law states that:

Point B on a typical stress-strain curve for a metal is called the:

Referring to a stress-strain curve, a material is said to be ductile if:

Materials that can sustain large strains and whose stress-strain curves show a very large elastic region but do not obey Hooke’s law over most of that region are classified as:

Young’s modulus (Y) is defined as the ratio of:

Given that steel has a Young’s modulus (Y) of 2.0 × 10¹¹ N m⁻² and copper has Y = 1.1 × 10¹¹ N m⁻², which material is considered more elastic?

For most common materials, the Shear Modulus (G) (or Modulus of Rigidity) is typically related to Young’s Modulus (Y) by the relation:

Compressibility (k) is defined as the fractional change in volume per unit increase in pressure, meaning k = ?

The elastic potential energy per unit volume (u) stored in a stretched wire, where σ is stress and ε is strain, is given by:

In structural engineering, I-shaped beams are commonly used because this section is highly effective in reducing bending by providing large depth d without excessive weight, since the sag (δ) is proportional to: