Units and Measurement

Which of the following sets of quantities have same dimensional formula ?

• Frequency, angular frequency and angular momentum

• Surface tension, stress and spring constant

• Work, energy and torque

• Thermal capacity, specific heat and entropy

A physical quantity P is related to four measurable quantities a, b, c and d as follows

         $\mathrm{P} = \frac{{\mathrm{a}}^3{\mathrm{b}}^2}{\sqrt{\mathrm{c}}\mathrm{d}}$

The percentage errors of measurement in a, b, c and d are 1 %, 3% ,4% and 2%. The percentage error in the quantity P is

• 10 %

• 13 %

• 5 %

• 15 %

The dimensional formula of magnetic flux is

• [M¹L⁰T^-2A^-1]

• [M¹L²T^-1A^-1]

• [M¹L²T^-2A^-1]

• [M¹L²T⁰A^-1]

A physical quantity A is related to four observables a, b, c and d as follows

                 $\mathrm{A} = \frac{{\mathrm{a}}^2{\mathrm{b}}^3}{\mathrm{c}\sqrt{\mathrm{d}}}$

The percentage errors of measurement in a, b, c and d are 1 %, 3%, 2% and 2% respectively. What is the percentage error in the quantity A ?

• 12 %

• 7 %

• 14 %

• 16 %

The dimensions of kinetic energy is

• [M²L²T¹]

• [M¹L²T¹]

• [M¹L²T^-2]

• [M¹L²T^-1]

In an experiment to measure the height of a bridge by dropping stone into water underneath if the error in measurement of time is 0.1 s at the end of 2 s, then the error in estimation of height of bridge will be

• 0.49 m

• 0.98 m

• 1.37 m

• 1.96 m

If the figure below represents a parabola, identify the physical quantities representing Y and X for constant acceleration

• X = time, Y = velocity

• X = velocity, Y = time

• X = time, Y = displacement

• X = time, Y = acceleration

If the velocity of light c, gravitational constant G and Planck's constant h are chosen as fundamental units, the dimensions of length L in the new system is

• [h¹c¹G^-1]

• [h^1/2c^1/2G^-1/2]

• [h¹c^-3G¹]

• [h^1/2c^-3/2G^1/2]

A plate has a length 5 ± 0.1 cm and breadth 2 ± 0.01 cm. Then the area of the plate is

• 10 ± 0.1 cm²

• 10 ± 0.01 cm²

• 10 ± 0.001 cm²

• 10 ± 1 cm²

If M = Mass, L = Length, T = Time and I = Electric current, then the dimensional formula for electrical resistance R is given by

• [R] = [M¹L²T^-3I^-2]

• [R] = [M¹L²T^-3I²]

• [R] = [M¹L²T³I^-2]

• [R] = [M¹L²T³I²]