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In an experiment for estimating the value of focal length of converging mirror, image of an object placed at \(40 \, \text{cm}\) from the pole of the mirror is formed at distance \(120 \, \text{cm}\) from the pole of the mirror. These distances are measured with a modified scale in which there are \(20\) small divisions in \(1 \, \text{cm}\). The value of error in measurement of focal length of the mirror is \( \frac{1}{K} \, \text{cm} \). The value of \( K \) is _______.

As shown in the figure, in an experiment to determine young’s modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of \( 45^\circ \) with the load axis. The length of wire is \( 62.8 \, \text{cm} \) and its diameter is \( 4 \, \text{mm} \). The Young’s modulus is found to be \( x \times 10^{4} \, \text{N} \, \text{m}^{-2} \). The value of \( x \) is ___________.

A \( 2 \, \text{meter} \) long scale with least count of \( 0.2 \, \text{cm} \) is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at \( 80 \, \text{cm} \) mark and \( 1 \, \text{m} \) mark, respectively. The image of the object pin on the other side of lens coincides with image pin that is kept at \( 180 \, \text{cm} \) mark. The \( \\% \) error in the estimation of focal length is:

In a screw gauge, there are \(100\) divisions on the circular scale and the main scale moves by \(0.5 \, \text{mm}\) on a complete rotation of the circular scale. The zero of circular scale lies \(6\) divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, \(4\) linear scale divisions are clearly visible while \(46^{\text{th}}\) division the circular scale coincide with the reference line. The diameter of the wire is _______ \( \times 10^{-2} \, \text{mm} \).

Match List I with List II

Choose the correct answer from the options given below:

A cylindrical wire of mass \( (0.4 \pm 0.01) \, \text{g} \) has length \( (8 \pm 0.04) \, \text{cm} \) and radius \( (6 \pm 0.03) \, \text{mm} \). The maximum error in its density will be:

Two transparent media having refractive indices \( 1.0 \) and \( 1.5 \) are separated by a spherical refracting surface of radius of curvature \( 30 \, \text{cm} \). The centre of curvature of surface is towards denser medium and a point object is placed on the principle axis in rarer medium at a distance of \( 15 \, \text{cm} \) from the pole of the surface. The distance of image from the pole of the surface is ______ \( \text{cm} \).

The momentum of a body is increased by \( 50\% \). The percentage increase in the kinetic energy of the body is ________ \( \% \).

Two resistances are given as \( R_{1} = (10 \pm 0.5)\, \Omega \) and \( R_{2} = (15 \pm 0.5)\, \Omega \). The percentage error in the measurement of equivalent resistance when they are connected in parallel is:

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JEE Main 2023 8th April Morning Shift

A cylindrical wire of mass \( (0.4 \pm 0.01) \, \text{g} \) has length \( (8 \pm 0.04) \, \text{cm} \) and radius \( (6 \pm 0.03) \, \text{mm} \). The maximum error in its density will be: