A straight magnetic strip has a magnetic moment of \(44 \mathrm{Am}^2\). If the strip is bent in a semicircular shape, its magnetic moment will be _______\(\mathrm{Am}^2\) \(\left(\right.\) Given \(\left.\pi=\frac{22}{7}\right)\)

A particle is moving in a circular path of radius \(a,\) with a constant velocity \(v\) as shown in the figure.The centre of circle is marked by \('C'\). The angular momentum from the origin \(O\) can be written as

Speed of a transverse wave on a straight wire (mass \(6.0\; \mathrm{g}\), length \(60\; \mathrm{cm}\) and area of cross-section \(1.0\; \mathrm{mm}^{2}\) ) is \(90\; \mathrm{ms}^{-1} .\) If the Young's modulus of wire is \(16 \times 10^{11}\; \mathrm{Nm}^{-2},\) the extension of wire over its natural length is

If speed \(V,\) area \(A\) and force \(F\) are chosen as fundamental units, then the dimension of Young's modulus will be :

The position of the centre of mass of a uniform semi-circular wire of radius \('R'\) placed in \(x-y\) plane with its centre at the origin and the line joining its ends as \(x\)-axis is given by \(\left(0, \frac{x R}{\pi}\right)\). Then, the value of \(|x|\) is ...... .

A body is in simple harmonic motion with time period half second \((T\, = 0.5\, s)\) and amplitude one \(cm\, (A\,= 1\, cm)\). Find the average velocity in the interval in which it moves form equilibrium position to half of its amplitude .... \(cm/s\)

One side of an equilateral prism is painted by a transparent material of refractive index \(n_2\). The refractive index of prism is \(1.6\). The minimum value of \(n_2\) required for total internal reflection from painted face is _______.

The equivalent capacitance between \(A\) and \(B\) in the circuit given below is.....\(μF\)

Heat energy of \(184\,kJ\) is given to ice of mass \(600\,g\) at \(-12^{\circ}\,C\), Specific heat of ice is \(2222.3\,J\,kg ^{-1^{\circ}}\,C ^{-1}\) and latent heat of ice in \(336\,kJ / kg ^{-1}\) \((A)\) Final temperature of system will be \(0^{\circ} C\). \((B)\) Final temperature of the system will be greater than \(0^{\circ} C\). \((C)\) The final system will have a mixture of ice and water in the ratio of \(5: 1\). \((D)\) The final system will have a mixture of ice and water in the ratio of \(1: 5\). \((E)\) The final system will have water only. Choose the correct answer from the options given below:

A thin ring of \(10\, cm\) radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of \(40\,\pi \,rad\,{s^{ - 1}}\) about its axis, perpendicular to its plane. If the magnetic field at its centre is \(3.8 \times {10^{ - 9}}\,T\), then the charge carried by the ring is close to \(\left( {{\mu _0} = 4\pi  \times {{10}^{ - 7}}\,N/{A^2}} \right)\)

If \(2^{10}+2^{9} \cdot 3^{1}+28 \cdot 3^{2}+\ldots+2 \cdot 3^{9}+3^{10}=S -211\) then \(S\) is equal to

Let the foci of the ellipse \(\frac{x^{2}}{16}+\frac{y^{2}}{7}=1\) and the hyperbola \(\frac{ x ^{2}}{144}-\frac{ y ^{2}}{\alpha}=\frac{1}{25}\) coincide. Then the length of the latus rectum of the hyperbola is:-

Let \(S\) be the set of all values of \(a_1\) for which the mean deviation about the mean of \(100\) consecutive positive integers \(a _1, a _2, a _3, \ldots ., a _{100}\) is \(25\). Then \(S\) is