JEE MainsJEE AdvanceBITSAT

JEE Mains | PYQ

The diameter of a wire measured by a screw gauge of least count \( 0.001 \,\text{cm} \) is \( 0.08 \,\text{cm} \). The length measured by a scale of least count \( 0.1 \,\text{cm} \) is \( 150 \,\text{cm} \). When a weight of \( 100 \,\text{N} \) is applied to the wire, the extension in length is \( 0.5 \,\text{cm} \), measured by a micrometer of least count \( 0.001 \,\text{cm} \). The error in the measured Young’s modulus is \( \alpha \times 10^{9} \,\text{N}/\text{m}^{2} \). The value of \( \alpha \) is ______. (Ignore the contribution of the load to Young’s modulus error calculation)

In a vernier callipers, \( 50 \) vernier scale divisions are equal to \( 48 \) main scale divisions. If one main scale division \( = 0.05 \, \text{mm} \), then the least count of the vernier callipers is ____________ \( \text{mm} \).

In a screw gauge when the circular scale is given five complete rotations it moves linearly by \( 2.5 \, \text{mm} \). If the circular scale has \( 100 \) divisions, the least count of screw gauge is ______ \( \text{mm} \).

In an experiment the values of two spring constants were measured as \( k_1 = (10 \pm 0.2) \, \text{N/m} \) and \( k_2 = (20 \pm 0.3) \, \text{N/m} \). If these springs are connected in parallel, then the percentage error in equivalent spring constant is:

When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, \( 4^{\text{th}} \) mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes \( 15 \) divisions on main scale and \( 5^{\text{th}} \) division of vernier scale coincides with a main scale division. Measured length of cylinder is ________ \( \text{mm} \). (Least count of Vernier calliper = \( 0.1 \, \text{mm} \))

The density \( \rho \) of a uniform cylinder is determined by measuring its mass \( m \), length \( l \) and diameter \( d \). The measured values of \( m \), \( l \) and \( d \) are \( 97.42\pm0.02 \, \text{g} \), \( 8.35\pm0.05 \, \text{mm} \) and \( 20.20\pm0.02 \, \text{mm} \), respectively. Calculated percentage fractional error in \( \rho \) is ______.

In a screw gauge the zero of main scale reference line coincides with the fifth division of the circular scale when two studs are in contact. There are \( 100 \) divisions in circular scale and pitch of screw gauge is \( 0.1 \, \text{mm} \). When diameter of a sphere is measured, the reading of main scale is \( 5 \, \text{mm} \) and \( 50^{\text{th}} \) division of circular scale coincides with the reference line of main scale. The diameter of sphere is ________ \( \text{mm} \).

In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and \( 7^{\text{th}} \) Vernier division coincides with a main scale reading. If the value of \( 1 \) main scale division is \( 1 \, \text{mm} \) and there are \( 10 \) Vernier scale divisions, then the Vernier caliper has

Four persons measure the length of a rod as \( 20.00 \, \text{cm} \), \( 19.75 \, \text{cm} \), \( 17.01 \, \text{cm} \) and \( 18.25 \, \text{cm} \). The relative error in the measurement of average length of the rod is:

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 \( 1 \, \text{mm} \) and the circular scale reading is \( 51 \) then the correct thickness of the sheet is ______ \( \text{mm} \). [Assume least count is \( 0.01 \, \text{mm} \)]

To compare EMF of two cells using potentiometer the balancing lengths obtained are \( 200 \, \text{cm} \) and \( 150 \, \text{cm} \). The least count of scale is \( 1 \, \text{cm} \). The percentage error in the ratio of EMFs is ______.

In an experiment to determine the resistance of a given wire using Ohm's law, the voltmeter and ammeter readings are noted as \( 10\,\mathrm{V} \) and \( 5\,\mathrm{A} \), respectively. The least counts of voltmeter and ammeter are \( 500\,\mathrm{mV} \) and \( 200\,\mathrm{mA} \), respectively. The estimated error in the resistance measurement is __________ \( \Omega \) .