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 a copper wire is stretched to increase its length by \(20 \% \). The percentage increase in resistance of the wire is \(..........\%\)

A parallel plate capacitor with width \(4\,cm\), length \(8\,cm\) and separation between the plates of \(4\,mm\) is connected to a battery of \(20\,V\). A dielectric slab of dielectric constant \(5\) having length \(1\,cm\), width \(4\,cm\) and thickness \(4\,mm\) is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be......... \(\in_{0}\,J\). (Where \(\epsilon_{0}\) is the permittivity of free space)

Moment of inertia of a square plate of side \(l\) about the axis passing through one of the corner and perpendicular to the plane of square plate is given by

A dipole with two electric charges of \(2 \mu \mathrm{C}\) magnitude each, with separation distance \(0.5 \mu \mathrm{~m}\), is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by \(30^{\circ}\) from the axis, it tends to realign in the direction due to a torque. The value of torque is :

What is the half-life (in years) period of a radioactive material if its activity drops to \(1 / 16^{\text {th }}\) of its initial value of \(30\) years?

The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure What is the value of current at \(t = 4\,s\) ? ............... \(\mu  A\)

A beam of protons with speed \(4 \times 10^{5}\, ms ^{-1}\) enters a uniform magnetic field of \(0.3\, T\) at an angle of \(60^{\circ}\) to the magnetic field. The pitch of the resulting helical path of protons is close to....\(cm\) (Mass of the proton \(=1.67 \times 10^{-27}\, kg\), charge of the proton \(=1.69 \times 10^{-19}\,C\))

Two coaxial discs, having moments of inertia \(I_1\) and \(\frac{I_1}{2}\) are a rotating with respectively angular velocities \(\omega_1\) and \(\frac{\omega_1}{2}\), about their common axes. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If \(E_f\) and \(E_i\) are the final and initial total energies, then \((E_f -E_i)\) is

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