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The maximum error in the measurement of resistance, current and time for which current flows in a n electrical circuit are \( 1\% \), \( 2\% \) and \( 3\% \) respectively. The maximum percentage error in the detection of the dissipated heat will be:

A torque meter is calibrated to reference standard of mass, length and time each with \( 5\% \) accuracy. After calibration, the measured torque with this torque meter will have net accuracy of:

A travelling microscope has \( 20 \) divisions per \( \text{cm} \) on the main scale while its vernier scale has total \( 50 \) divisions and \( 25 \) vernier scale divisions are equal to \( 24 \) main scale divisions, what is the least count of the travelling microscope?

In a Vernier Calipers, \( 10 \) divisions of Vernier scale is equal to the \( 9 \) divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and \( 4{\text{th}} \) Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to \( 1 \, \text{mm} \). While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between \( 30 \) and \( 31 \) divisions of main scale reading and \( 6{\text{th}} \) Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be:

In a vernier callipers, each \( \mathrm{cm} \) on the main scale is divided into \( 20 \) equal parts. If tenth vernier scale division coincides with ninth main scale division. Then the value of vernier constant will be __________ \( \times 10^{-2} \,\mathrm{mm} \).

In van dar Wall equation \( \left[P + \dfrac{a}{V^{2}}\right]\left[V - b\right] = R T \); \( P \) is pressure, \( V \) is volume, \( R \) is universal gas constant and \( T \) is temperature. The ratio of constants \( \dfrac{a}{b} \) is dimensionally equal to:

In experiment to find out the diameter of wire using screw gauge, the following observations were noted:

(a) Screw moves \( 0.5 \, \text{mm} \) on main scale in one complete rotation
(b) Total divisions on circular scale \( = 50 \)
(c) Main scale reading is \( 2.5 \, \text{mm} \)
(d) \( 45^{\text{th}} \) division of circular scale is in the pitch line
(e) Instrument has \( 0.03 \, \text{mm} \) negative error
Then the diameter of wire is

A travelling microscope is used to determine the refractive index of a glass slab. If \( 40 \) divisions are there in \( 1 \, \text{cm} \) on main scale and \( 50 \) Vernier scale divisions are equal to \( 49 \) main scale divisions, then least count of the travelling microscope is _______ \( \times 10^{-6} \, \text{m} \).

The one division of main scale of Vernier calipers reads \( 1 \, \text{mm} \) and \( 10 \) divisions of Vernier scale is equal to the \( 9 \) divisions on main scale. When the two jaws of the instrument touch each other, the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between \( 4.1 \, \text{cm} \) and \( 4.2 \, \text{cm} \) and \( 6^{\text{th}} \) Vernier division coincides with a main scale division. The diameter of the bob will be ______ \( \times 10^{-2} \, \text{cm} \).

Consider the efficiency of carnot’s engine is given by \( \eta = \displaystyle\frac{\alpha \beta}{\sin \theta} \log_e \frac{\beta x}{k T} \), where \( \alpha \) and \( \beta \) are constants If \( T \) is temperature, \( k \) is Boltzmann constant, \( \theta \) is angular displacement and \( x \) has the dimensions of length. Then, choose the incorrect option.

A silver wire has a mass \( (0.6 \pm 0.006) \, \text{g} \), radius \( (0.5 \pm 0.005) \, \text{mm} \) and length \( (4 \pm 0.04) \, \text{cm} \). The maximum percentage error in the measurement of its density will be:

The Vernier constant of Vernier calipers is \( 0.1 \, \text{mm} \) and it has zero error of \( (-0.05) \, \text{cm} \). While measuring diameter of a sphere, the main scale reading is \( 1.7 \, \text{cm} \) and coinciding Vernier division is \( 5 \). The corrected diameter will be _______ \( \times 10^{-2} \, \text{cm} \).

In an experiment to find acceleration due to gravity \( (g) \) using simple pendulum, time period of \( 0.5 \, \text{s} \) is measured from time of \( 100 \) oscillation with a watch of \( 1 \, \text{s} \) resolution. If measured value of length is \( 10 \, \text{cm} \) known to \( 1 \, \text{mm} \) accuracy. The accuracy in the determination of \( g \) is found to be \( x\% \). the value of \( x \) is:

A screw gauge of pitch \( 0.5 \, \text{mm} \) is used to measure the diameter of uniform wire of length \( 6.8 \, \text{cm} \), the main scale reading is \( 1.5 \, \text{mm} \) and circular scale reading is \( 7 \). The calculated curved surface area of wire to appropriate significant figures is:
[Screw gauge has \( 50 \) divisions on its circular scale]

If \( Z = \frac{A^2 B^3}{C^4} \), then the relative error in \( Z \) will be:

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JEE Main 2022 25th June Morning Shift

If \( Z = \frac{A^2 B^3}{C^4} \), then the relative error in \( Z \) will be: