JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Units & Measurement

WhatsApp Email

A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm , respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be

\frac{x}{100}

where x is

____

Answer: 3

Solution

The least count of the screw gauge is

L C = \frac{pitch}{no. of circular divisions} = \frac{0.75 mm}{15} = 0.05 mm

This is the absolute error in each linear measurement, so

Δ L = Δ B = 0.05

mm, with

L = 5

mm and

B = 2.5

mm.

For area

A = L B

, the maximum fractional error adds:

\frac{Δ A}{A} = \frac{Δ L}{L} + \frac{Δ B}{B} = \frac{0.05}{5} + \frac{0.05}{2.5} = \frac{1}{100} + \frac{2}{100} = \frac{3}{100}

x = 3

JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Integer answer

Practise more: all JEE Main PYQs on Units & Measurement →

More JEE Main questions on Units & Measurement

If ε, E and t represent the free space permittivity, electric field and time respectively, then the unit of $\frac{εE}{t}$ will be :
JEE Main 2026View solution →
Keeping the significant figures in view, the sum of the physical quantities $52.01 m, 153.2 m$ and 0.123 m is :
JEE Main 2026View solution →
A spherical body of radius $r$ and density $σ$ falls freely through a viscous liquid having density $ρ$ and viscosity $η$ and attains a terminal velocity $v_{0}$ . Estimated maximum error in the quantity $η$ is : (Ignore errors associated with …
JEE Main 2026View solution →
Four persons measure the length of a rod as $20.00 cm$ , $19.75 cm$ , $17.01 cm$ and $18.25 cm$ . The relative error in the measurement of average length of the rod is:
JEE Main 2026View solution →
In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and the circular scale reading is 51 then the …
JEE Main 2026View solution →
A ball of radius r and density $ρ$ dropped through a viscous liquid of density $σ$ and viscosity $η$ attains its terminal velocity at time t, given by $t = A ρ^{a} r^{b} η^{c} σ^{d}$ , where A is a constant and a, b, c and d are integers. The value of $\frac{b + c}{a + d}$ …
JEE Main 2026View solution →