Physics

The period T of a circular motion is the time taken to complete one full revolution. It is given by the circumference of the circle (2πr) divided by the speed v, hence T = 2πr/v.

When a length is measured as 6200 mm with a meter rod, which typically has precision to the nearest millimeter or centimeter, the trailing zeros without a decimal point are not considered significant. Thus, the number 6200 has 2 significant figures (6 and 2).

After completing two full revolutions around a circle, the displacement (straight-line distance from start to end point) is zero because the starting and ending points coincide. However, the path length covered is the circumference times two. Thus, the ratio of displacement to path length is 0.

An ideal fluid is a theoretical concept in fluid mechanics that is non-viscous, incompressible, and exhibits steady flow, meaning it possesses all these properties simultaneously. Therefore, option D correctly states that an ideal fluid possesses all these properties.

One light year is the distance that light travels in one year in vacuum. It is exactly 9.46073 × 10^15 meters, which is equivalent to about 9.46073 × 10^12 kilometers (approximately 9.46 trillion kilometers). Therefore, the correct option must have the unit meters with the value close to 9.5 × 10^15. Option A correctly states 9.5 × 10^15 meters, which is the closest and accurate representation of one light year. Option C incorrectly states 9.5 × 10^15 kilometers, which is off by a factor of 1000. Hence, the correct answer is A.

The SI unit of frequency is the hertz (Hz), which represents one cycle per second. Other options like vibration s⁻², radian, and ms⁻¹ are units for different physical quantities.

The SI unit of force is the Newton, which is a proper noun and should be capitalized. Its symbol is 'N', also capitalized. Therefore, the correct pair is 'Newton, N'.

For a particle moving in a circle with angular velocity $\omega$, the acceleration of its projection on the diameter (x-axis) is given by $a=-{\omega }^{2}x$. The negative sign indicates direction, but since options do not show signs, the magnitude is ${\omega }^{2}x$. Option A correctly represents this as "w2x" (interpreted as ${\omega }^{2}x$).

The linear speed v of a point on the rim of a wheel is given by v = circumference × revolutions per second. The wheel diameter is 1 m, so the circumference is π × 1 = π meters. The wheel makes 30 revolutions per minute, which is 30/60 = 0.5 revolutions per second. Therefore, the linear speed is π × 0.5 = π/2 meters per second. Hence, the correct answer is option B (π/2).

The centripetal force required to keep a body moving in a circle of radius r at linear speed V is given by F = mV²/r, where m is the mass of the body. This force acts towards the center of the circle.

Reducing uncertainty in timing experiments can be achieved by using highly precise instruments to improve measurement accuracy and by counting the number of vibrations to increase the total measured time, thereby reducing relative error. Both methods together help minimize timing uncertainty.

A satellite orbiting the Earth is accelerating due to the centripetal force acting towards the Earth, making its frame of reference non-inertial. Inertial frames are those that are either at rest or move with constant velocity, without acceleration.

When a body moves in a circle, its linear velocity is tangent to the circle, while its angular velocity vector points along the axis of rotation (perpendicular to the plane of motion). Therefore, the angle between linear velocity and angular velocity is always 90°.

The span (horizontal distance) of a broad jump depends primarily on the angle of projection, as it determines the trajectory and range of the jump. Other factors like mass or height of jump do not directly determine the horizontal distance covered.

The shape of an airplane wing that generates lift is called an aerofoil (or airfoil) profile. This design allows air to flow faster over the top surface, creating lower pressure and thus lift.

In a Venturi meter, the fluid speed is maximum at the throat, which is the narrowest part of the meter. According to the principle of continuity, the velocity increases where the cross-sectional area decreases.

At the highest point in vertical circular motion, the tension in the string is less than the weight of the stone because the weight provides part of the centripetal force needed to keep the stone moving in a circle. The tension is not zero unless the stone is just about to lose contact, and it is not equal to or maximum compared to the weight at the top position.

A geostationary satellite orbits the Earth once every 24 hours, matching the Earth's rotation period, which allows it to remain fixed over one position on the equator.

In simple harmonic motion, the total energy of the system is proportional to the square of the amplitude because energy depends on both kinetic and potential energy, which are proportional to the square of displacement (amplitude).

Fundamental science is often considered to have two main frontiers: the frontier of the very large (cosmology, astrophysics) and the frontier of the very small (particle physics, quantum mechanics). Therefore, the correct answer is 2.

For small droplets falling through air, the terminal velocity is proportional to the square of the radius of the droplet. Given the radii ratio of 2:3, the terminal velocity ratio is (2^2):(3^2) = 4:9. Among the options, '4:09' (option B) correctly represents this ratio. The original answer '4:06' (option A) is incorrect and likely a typographical error.

Laminar flow typically occurs at low flow speeds where the fluid moves in smooth, orderly layers without turbulence. At higher speeds, flow tends to become turbulent.

The rotational kinetic energy of a rotating object is given by K.E = (1/2) I ω², where I is the moment of inertia and ω is the angular velocity. For a hoop, the moment of inertia about its central axis is I_hoop = MR². For a solid disc, the moment of inertia is I_disc = (1/2) MR². Given the same mass, radius, and angular velocity, the hoop's rotational kinetic energy is K.E_hoop = (1/2)(MR²)ω² = (1/2)MR²ω², while the disc's rotational kinetic energy is K.E_disc = (1/2)((1/2)MR²)ω² = (1/4)MR²ω². Therefore, K.E_hoop = 2 × K.E_disc. Hence, the hoop has twice the rotational kinetic energy of the disc when both rotate at the same angular velocity.

Electric charge is a derived quantity in the SI system because it is defined in terms of the base unit electric current (ampere) multiplied by time (second). Electric current, plane angle, and amount of substance are base quantities or dimensionless quantities.

The speed of efflux of a fluid from an orifice can be determined using Torricelli's theorem, which relates the speed to the height of the fluid column. Bernoulli's theorem is a more general principle from which Torricelli's theorem can be derived, but Torricelli's theorem specifically addresses efflux speed. The 'Venture relation' is not relevant here, and 'All' is incorrect because not all options apply.