A hole is drilled in a metal sheet. At \(27^{\circ} C\), the diameter of hole is 5 cm . When the sheet is heated to \(177^{\circ} C\), the change in the diameter of hole is \(d \times 10^{-3} cm\). The value of \(d\) will be ________ , if coefficient of linear expansion of the metal is \(1.6 \times 10^{-5} /{ }^{\circ} C\)

An infinitely long straight wire carrying current \(I,\) one side opened rectangular loop and a conductor \(C\) with a sliding connector are located in the same plane, as shown in the figure. The connector has length \(l\) and resistance \(R\). It slides to the right with a velocity \(V.\) The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation \(r,\) between the connector and the straight wire is

Two moles of an ideal gas with \(\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{5}{3}\) are mixed with \(3\) moles of another ideal gas with \(\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{4}{3} .\) The value of \(\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}\) for the mixture is

The angle between vector \(\vec{Q}\) and the resultant of \((2 \overrightarrow{\mathrm{Q}}+2 \overrightarrow{\mathrm{P}})\) and \((2 \overrightarrow{\mathrm{Q}}-2 \overrightarrow{\mathrm{P}})\) is _______.

A wire carrying current \(I\) is bent in the shape \(A\,B\,C\,D\,E\,F\,A\) as shown, where rectangle \(A\,B\,C\,D\,A\) and \(A\,D\,E\,F\,A\) are perpendicular to each other. If the sides of the rectangles are of lengths \(a\) and \(b,\) then the magnitude and direction of magnetic moment of the loop \(A\,B\,C\,D\,E\,F\,A\,\) is

A wire carrying current \(I\) is tied between points \(P\) and \(Q\) and is in the shape of a circular arc of radius \(R\) due to a uniform magnetic field \(B\) (perpendicular to the plane of the paper, shown by \(\times \times \times \)) in the vicinity of the wire. If the wire subtends an angle \(2\theta_0\) at the centre of the circle (of which it forms an arc) then the tension in the wire is

Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m . They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process _________ J.

In a series \(L R\) circuit \(X_{L}=R\) and power factor of the circuit is \(P _{1}\). When capacitor with capacitance \(C\) such that \(X _{ L }= X _{ C }\) is put in series, the power factor becomes \(P_{2}\). The ratio \(\frac{ P _{1}}{ P _{2}}\) is

The charge stored by the capacitor C in the given circuit in the steady state is _________ \(\mu C\).

A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of \(10 \pi \mathrm{rad} \mathrm{s}^{-1}\) about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim ? \((\pi=3.14)\)