Physics

For a hoop rolling without slipping, its rotational kinetic energy equals its translational kinetic energy because the moment of inertia is I = MR², and rotational KE = (1/2)Iω² = (1/2)MR²(ω²). Since v = ωR, this equals (1/2)Mv², which is the translational kinetic energy.

According to Einstein's theory of general relativity, gravity affects all forms of energy and momentum, including material objects and electromagnetic radiation (light). Therefore, gravitational interaction is possible between material objects and electromagnetic radiation.

A cyclist skids when the required centripetal force to maintain circular motion exceeds the maximum frictional force (limiting friction) available between the tyres and the road. This causes the tyres to lose grip and skid outward.

The decrease in pressure with an increase in fluid speed in a horizontal pipe is described by Bernoulli's principle, often called the Bernoulli effect. The Venturi effect is a specific application of Bernoulli's principle involving a constricted pipe section, but the general phenomenon is Bernoulli's effect.

In vibratory motion, such as simple harmonic motion, the total mechanical energy (sum of potential and kinetic energy) remains constant if there is no damping or external force. This is because energy continuously transforms between kinetic and potential forms without loss.

One torr is defined as exactly 1/760 of a standard atmosphere. Since one atmosphere is defined as 101325 pascals (N/m²), one torr equals 101325/760 pascals, which is approximately 133.322 pascals (N/m²). Therefore, option A, '133.3 Nm-2', correctly represents one torr. Note that the unit should be written as N/m² (newtons per square meter), which is equivalent to pascals (Pa).

When an elevator accelerates upward with acceleration a, the apparent weight increases by ma, making it mg + ma. This is because the normal force must counteract both gravity and the upward acceleration.

In turbulent flow, fluid particles move chaotically and irregularly, making it impossible to track their exact paths. In contrast, laminar flow features smooth, orderly layers where particle paths are well-defined and trackable.

The distance moved by a point on the rim of a wheel turning through an angle is the arc length of the circle segment described by that angle. The arc length s is given by s = r × θ, where θ is the angle in radians. Since 30° equals π/6 radians, the arc length is s = r × (π/6) = (π r)/6. Therefore, the correct option is B: π/6 × r.

The flow of an ideal fluid is always streamline (or laminar) because ideal fluids are non-viscous and incompressible, which prevents turbulence and irregular flow patterns.