Joint Entrance Examination

Graduate Aptitude Test in Engineering

1

Subjective

The side of a cube is measured by vernier callipers (10 divisions of a vernier scale coincide with
9 divisions of main scale, where 1 division of main scale is 1 mm). The main scale reads 10 mm and
first division of vernier scale coincides with the main scale. Mass of the cube is 2.736 g. Find the
density of the cube in appropriate significant figures.

2.66 gm/cm^{3}

2

Subjective

A screw gauge having 100 equal divisions and a pitch of length 1 mm is used to measure the diameter of a wire of length 5.6 cm. The main scale reading is 1mm and 47^{th} circular division coincides
with the main scale. Find the curved surface area of wire in cm^{2} to appropriate significant figures. ( use $$\pi = {{22} \over 7}$$ )

2.6 cm^{2}

The distance moved on the linear scale when circular scale makes one complete rotation is p = 1 mm (pitch). The number of divisions on the circular scale is N = 100. Thus, one division on the circular scale is LC = $${p \over N} = {1 \over {100}}$$ = 0.01 mm. The linear scale reading (LSR) is 1 mm and the circular scale reading (CSR) is 47. Thus, the diameter of the wire is

d = LSR + CSR $$\times$$ LC

= 1 + 47 $$\times$$ 0.01 = 1.47 mm = 0.147 cm.

The curved surface area is S = 2$$\pi$$rL. That is,

$$S = 2\pi \left( {{d \over 2}} \right)L$$

$$S = \pi dL = \pi \left( {{{1.47} \over {10}}} \right)5.6 = $$ 2.5848 cm^{2} = 2.6 cm^{2}

which is corrected to two significant digits.

d = LSR + CSR $$\times$$ LC

= 1 + 47 $$\times$$ 0.01 = 1.47 mm = 0.147 cm.

The curved surface area is S = 2$$\pi$$rL. That is,

$$S = 2\pi \left( {{d \over 2}} \right)L$$

$$S = \pi dL = \pi \left( {{{1.47} \over {10}}} \right)5.6 = $$ 2.5848 cm

which is corrected to two significant digits.

3

Subjective

In Searle's experiment, which is used to find Young's Modulus of elasticity, the diameter of experimental wire is D = 0.05 cm ( measured by a scale of least count 0.001 cm ) and length is L = 110 cm ( measured by a scale of least count 0.1 cm ). A weight of 50 N causes an extension of X = 0.125 cm (measured by a micrometer of least count 0.001 cm ). Find maximum possible error in the value of Young's modulus. Screw gauge and and meter scale are free from error.

1.09 $$ \times $$ 10^{10} N/m^{2}

4

Subjective

If n^{th} divisions of the main scale coincide with (n+1)^{th} divisions
of vernier scale. Given one main scale division is equal to 'a' units. Find the
least count of the vernier.

$${a \over {n + 1}}units$$

We know that (n + 1) divisions on the vernier scale = n division on the main scale

Therefore,

1 division on the vernier scale = $$\left( {{n \over {n + 1}}} \right)$$ divisions on the main scale = $$\left( {{n \over {n + 1}}} \right)a$$ units

Therefore, the least count (LC) of the vernier caliper is

$$1(MSD) - 1(VSD) = a - \left( {{n \over {n + 1}}} \right)a = {a \over {n + 1}}$$

Therefore,

1 division on the vernier scale = $$\left( {{n \over {n + 1}}} \right)$$ divisions on the main scale = $$\left( {{n \over {n + 1}}} \right)a$$ units

Therefore, the least count (LC) of the vernier caliper is

$$1(MSD) - 1(VSD) = a - \left( {{n \over {n + 1}}} \right)a = {a \over {n + 1}}$$

On those following papers in Subjective

Number in Brackets after Paper Indicates No. of Questions

IIT-JEE 2005 (1) *keyboard_arrow_right*

IIT-JEE 2004 (2) *keyboard_arrow_right*

IIT-JEE 2003 (1) *keyboard_arrow_right*

IIT-JEE 1990 (1) *keyboard_arrow_right*

IIT-JEE 1983 (1) *keyboard_arrow_right*

IIT-JEE 1982 (1) *keyboard_arrow_right*

IIT-JEE 1981 (1) *keyboard_arrow_right*

IIT-JEE 1980 (1) *keyboard_arrow_right*

Units & Measurements *keyboard_arrow_right*

Laws of Motion *keyboard_arrow_right*

Work Power & Energy *keyboard_arrow_right*

Impulse & Momentum *keyboard_arrow_right*

Rotational Motion *keyboard_arrow_right*

Gravitation *keyboard_arrow_right*

Properties of Matter *keyboard_arrow_right*

Heat and Thermodynamics *keyboard_arrow_right*

Waves *keyboard_arrow_right*

Motion *keyboard_arrow_right*

Electrostatics *keyboard_arrow_right*

Current Electricity *keyboard_arrow_right*

Electromagnetic Induction *keyboard_arrow_right*

Magnetism *keyboard_arrow_right*

Geometrical Optics *keyboard_arrow_right*

Wave Optics *keyboard_arrow_right*

Modern Physics *keyboard_arrow_right*

Dual Nature of Radiation *keyboard_arrow_right*

Atoms and Nuclei *keyboard_arrow_right*