Let \(l, r, c\) and \(v\) represent inductance, resistance, capacitance and voltage, respectively. The dimension of \(\frac {l}{rcv}\) in \(SI\,units\) will be

The speed of a transverse wave passing through a string of length \(50 \;cm\) and mass \(10\,g\) is \(60\,ms ^{-1}\). The area of cross-section of the wire is \(2.0\,mm ^{2}\) and its Young's modulus is \(1.2 \times 10^{11}\,Nm ^{-2}\). The extension of the wire over its natural length due to its tension will be \(x \times 10^{-5}\; m\). The value of \(x\) is \(...\)

Consider a finite insulated, uncharged conductor placed near a finite positively charged conductor. The uncharged body must have a potential

Distance of the centre of mass of a solid uniform cone from its vertex is \(z_0\) . If the radius of its base is \(R\) and its height is \(h\) then \(z_0\) is equal to

A galvanometer having a coil resistance \(100 \;\Omega\) gives a full scale deflection when a current of \(1 \;\mathrm{mA}\) is passed through it. What is the value of the resistance which can convert this galvanometer into a voltmeter giving full scale deflection for a potential difference of \(10\; \mathrm{V} ?\)......\(k\Omega\)

A solid sphere of radius \(R\) carries a charge \((Q+q)\) distributed uniformly over its volume. A very small point like piece of it of mass \(m\) gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge \(q.\) If it acquires a speed \(v\) when it has fallen through a vertical height \(y\) (see figure), then : (assume the remaining portion to be spherical).

In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division \(=0.05 mm\), then the least count of the vernier callipers is _________ mm.

A small circular loop of wire of radius \(a\) is located at the centre of a much larger circular wire loop of radius \(b\). The two loops are in the same plane. The outer loop of radius \(b\) carries an alternating current \(I = I_0\, cos\, (\omega t)\) . The emf induced in the smaller inner loop is nearly

The total current supplied to the circuit as shown in figure by the \(5 V\) battery is \(A\)