One of the two identical conducing wires of length \(L\) is bent in the form of a circular loop and the other one into a circular coil of \(N\) identical turns. If the same current is passed in both, the ratio of the magnetic field at the central of the loop \((B_L)\) to that at the centre of the coil \((B_C),\); \(.\,\frac {B_L}{B_C}\) will be

There are \(100\) divisions on the circular scale of a screw gauge of pitch \(1 \mathrm{~mm}\). With no measuring quantity in between the jaws, the zero of the circular scale lies \(5\) divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found the \(4\) linear scale divisions are clearly visible while \(60\) divisions on circular scale coincide with the reference line. The diameter of the wire is _______.

charge \(Q\) is uniformly distributed over a long rod \(AB\) of length \(L\) as shown in the figure. The electric potential at the point \(O\) lying at distance \(L\) from the end \(A\) is

A conducting wire of length \( l\) area of cross-section \(A\) and electric resistivity \(\rho\) is connected between the terminals of a battery. \(A\) potential difference \(V\) is developed between its ends, causing an electric current.If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be

Four capacitor each of capacitance \(16 \mu \mathrm{~F}\) are connected as shown in the figure. The capacitance between points A and B is : ______ (in \(\mu \mathrm{F}\)).

A square loop of side \(15 \mathrm{~cm}\) being moved towards right at a constant speed of \(2 \mathrm{~cm} / \mathrm{s}\) as shown in figure. The front edge enters the \(50 \mathrm{~cm}\) wide magnetic field at \(t=0\). The value of induced emf in the loop at \(t=10 \mathrm{~s}\) will be _______.

A rigid massless road of length \(3l\) has tow masses attached at each end as shown in the figure. The rod is pivoted at point \(P\) on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be

Two discs have moments of intertia \({I}_{1}\) and \({I}_{2}\) about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, \(\omega_{1}\) and \(\omega_{2}\) respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by :

A piece of wood from a recently cut tree shows \(20\,decays\) per minute. A wooden piece of same size placed in a museum ( obtained from a tree cut many years back) shows \(2\,decays\) per minute. If half life of \(C^{14}\) is \(5730\, years\), then age of the wooden piece placed in the museum is approximately ........... \(years\)

A particle executes simple harmonic motion between \(x =- A\) and \(x =+ A\). If time taken by particle to go from \(x=0\) to \(\frac{A}{2}\) is \(2 s\); then time taken by particle in going from \(x =\frac{ A }{2}\) to \(A\) is \(.........\,s\)

The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between \(t=0\) to \(t=4 \mathrm{~s}\) ?

Four identical rectangular plates with length, \(l=2\, cm\) and breadth, \(b =\frac{3}{2}\, cm\) are arranged as shown in figure. The equivalent capacitance between \(A\) and \(C\) is \(\frac{ x \varepsilon_{0}}{ d } .\) The value of \(x\) is (Round off to the Nearest Integer)

Following gates section is connected in a complete suitable circuit. For which of the following combination, bulb will glow \((ON)\)?