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 :

For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is \(\frac{x}{5}\). The value of \(x\) is ................

A hollow cylindrical conductor has length of \(3.14\,m\), while its inner and outer diameters are \(4\,mm\) and \(8\,mm\) respectively. The resistance of the conductor is \(n \times 10^{-3}\,\Omega\).If the resistivity of the material is \(2.4 \times 10^{-8}\,\Omega\,m\). The value of \(n\) is \(..........\)

Two discs of same mass and different radii are made of different materials such that their thicknesses are \(1\,cm\) and \(0.5\,cm\) respectively. The densities of materials are in the ratio \(3: 5\). The moment of inertia of these discs respectively about their diameters will be in the ratio of \(\frac{x}{6}\). The value of \(x\) is \(.......\).

Two long parallel conductors \(S_{1}\) and \(S_{2}\) are separated by a distance \(10 \,cm\) and carrying currents of \(4\, A\) and \(2 \,A\) respectively. The conductors are placed along \(x\)-axis in \(X - Y\) plane. There is a point \(P\) located between the conductors (as shown in figure). A charge particle of \(3 \pi\) coulomb is passing through the point \(P\) with velocity \(\overrightarrow{ v }=(2 \hat{ i }+3 \hat{ j }) \,m / s\); where \(\hat{i}\) and \(\hat{j} \quad\) represents unit vector along \(x\) and \(y\) axis respectively. The force acting on the charge particle is \(4 \pi \times 10^{-5}(-x \hat{i}+2 \hat{j}) \,N\). The value of \(x\) is

A liquid drop of diameter \(2\) mm breaks into \(512\) droplets. The change in surface energy is \(\alpha \times 10^{-6}\) J. The value of \(\alpha\) is _______. (Take surface tension of liquid \(= 0.08\) N/m)

A thin convex lens of focal length 5 cm and a thin concave lens of focal length 4 cm are combined together (without any gap) and this combination has magnification \( m_{1} \), when an object is placed 10 cm before the convex lens. Keeping the positions of convex lens and object undisturbed a gap of 1 cm is introduced between the lenses by moving the concave lens away, which lead to a change in magnification of total lens system to \( m_{2} \).
The value of \(\left|\frac{m_1}{m_2}\right|\) is __________ .

Two blocks of mass \(2 \mathrm{~kg}\) and \(4 \mathrm{~kg}\) are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is \(4.0 \times 10^{-5}\) \(\mathrm{m}\) and Young's modulus of the metal is \(2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^2\). The longitudinal strain developed in the wire is \(\frac{1}{\alpha \pi}\). The value of \(\alpha\) is _______. [Use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) )

A thermometer graduated according to a linear scale reads a value \(x_0\) when in contact with boiling water, and \(x_0/3\) when in contact with ice. What is the temperature of an object in \({}^oC\), if this thermometer in the contact with the object reads \(x_0/2\) ?

If \(p\) and \(q\) are non-zero real numbers and \({\alpha ^3} + {\beta ^3} =  - p\), \(\alpha \beta  = q\), then a quadratic equation whose roots are \(\frac{{{\alpha ^2}}}{\beta },\frac{{{\beta ^2}}}{\alpha }\) is

As show in the figure, in steady state, the charge stored in the capacitor is....... \(\times 10^{-6}\,C\).

The equation \(\arg \left(\frac{\mathrm{z}-1}{\mathrm{z}+1}\right)=\frac{\pi}{4}\) represents a circle with:

A \(dc\) source of \(emf \,E_1 = 100\,V\) and internal resistance \(r = 0.5\,\Omega ,\) a storage battery of emf \(E_2 = 90\,V\) and an external resistance \(R\) are connected as shown in figure. For what value of \(R\) no current will pass through the battery ? ................ \(\Omega\)