Physical World & Measurement

Power delivered by a spring is given by P = (1/2)kx²/t. Check the dimensional consistency of this expression with the known dimension of power, [ML²T⁻³].

A system of units takes force, length, and time as fundamental, with 1 unit of force = 5 N, 1 unit of length = 4 m, and 1 unit of time = 2 s. Express 10 kg in terms of the new mass unit.

A quantity X = √A · B² / C³. The percentage errors in A, B, and C are 4%, 2%, and 1% respectively. Find the percentage error in X.

A vernier caliper (least count 0.01 cm) has a positive zero error of 0.03 cm. The main scale reads 4.2 cm and the 3rd vernier division coincides with a main scale line. Find the corrected reading.

Evaluate 3.24/1.2 to the correct number of significant figures.

The time period of a mass-spring system is believed to follow T = k·mᵃ·kᵇ (k here being the spring constant in the formula, and k the dimensionless constant outside). Using [spring constant] = [MT⁻²], find a and b.

Convert 1 watt of power into the CGS unit of power (erg/s).

Which of the following equations is dimensionally INCORRECT?

A quantity X = (A + B)/C, where A = (10 ± 0.1), B = (20 ± 0.2), and C = (5 ± 0.1) (all in consistent units). Find the percentage error in X.

What is the order of magnitude of the number of seconds in one year?

The universal gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg² in SI units. Find its value in a system where the unit of mass is 5 kg, the unit of length is 2 m, and the unit of time is 2 s.

The mass of a cube is measured with 2% error, and the length of its side is measured with 1% error. Find the percentage error in its calculated density.